#Interval Notation Class 11

[class11maths]

00:00:22 Introduction to Lecture 2 of Sets

00:01:32 Basics Explanation of Subsets

00:09:42 NCERT Exercise 1.3 Question 1

00:18:00 Detailed explanation and difference between subset & belongs to (Set belongs to another set)

00:37:32 NCERT Exercise 1.3 Question 2

00:42:52 NCERT Exercise 1.3 Question 3

00:48:52 Total number of subsets in a set (NCERT Exercise 1.3 Question 4)

00:55:12 Power Sets

00:58:12 NCERT Exercise 1.3 Question 5

01:01:32 Represent Real Numbers through closed and open intervals

01:10:32 NCERT Exercise 1.3 Question 6

01:12:02 NCERT Exercise 1.3 Question 7

01:14:42 Universal Sets

01:18:02 NCERT Exercise 1.3 Question 8

01:19:32 NCERT Exercise 1.3 Question 9

Master NCERT Exercise 1.3 of Sets (Class 11 Maths Chapter 1) with this detailed lecture by expert Ashish Sir from MathYug. Learn subsets, power sets, universal sets, and interval notation for real numbers with step-by-step solutions to all questions.

Download notes and assignments from https://mathyug.com/class-11-maths

Explore CBSE + IIT JEE Syllabus (in Hindi): https://mathyug.com

[the-music-keeper]

Do you remember the [very first] night of September?

Yes, I know those aren't the lyrics, but it's September 1 and I wanted a flashy title for the first to-do list of the semester!

There's something very special about this semester. For the first time in six years -- SIX YEARS, Y'ALL -- I'm taking a class that has nothing to do with music. *GASP* I know! Crazy! I'm kind of excited! However, as you will see, I will not be able to escape music completely in that class.

German

1. Review chapter 2. (With a highlighter and a notebook!)

2. Translate the practice sentences in chapter 2. (Building blocks.)

3. Translate the long passage in chapter 2. (It's on Bach. Of course I'd have to translate a passage on Bach.)

4. Make a Quizlet set. (There's a lot of vocab and while we're not being tested on it, knowing vocab will definitely make reading easier!)

Theory

5. Transcribe a chant selection into modern notation. (I'm also expected to make some comments.)

6. Write the intervals between the chant and the organum on another selection. (I was an overachiever.)

Doctoral Applications

7. Finish reading Music on the Move. (It's a textbook written by the potential advisor at Ohio State University, and I really want to make sure I finish reading it before I email her.)

8. Send introduction emails and requests to Zoom. (I get kind of lightheaded whenever I think about this task, which tells you just how anxious I am about doing this.)

Piano Practice

9. Finish learning the music for the semester. (All four pieces learned, although one needs some work.)

Adulting

10. Laundry. (All done!)

11. Keep an eye on my Allstate account. (I'm going to have to call. It's been a week and a half.)

12. Buy my train ticket home for a visit in early October. (My friend is getting married!)

13. Exercise period #1. (I did thirty minutes of stationary cycling!)

14. Exercise period #2. (Stationary bike and rowing machine.)

I was hoping to get some of this done this afternoon. I got some piano practice done, but after I got lunch I dealt with some other things and then ended up with a disgusting low that, despite treatment, has knocked me out (it doesn't help that I was out late last night, either). So I'm going to head back to the compound, eat food, and then see how I'm feeling. I really want to get some of this German homework done tonight.

[strangenewneighborhood]

wait u guys get signatures?? oh i guess thats on me, anyway, whats the meaning of the symbol on our necklace gordo? - 🐟

Hey, yeah, good question.

Examples of the symbolic use of lowercase lambda include:

Lambda indicates the wavelength of any wave, especially in physics, electronics engineering, and mathematics.[5]

In evolutionary algorithms, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from Evolution strategy notation.

Lambda indicates the radioactivity decay constant in nuclear physics and radioactivity. This constant is very simply related (by a multiplicative constant) to the half-life of any radioactive material.

In probability theory, lambda represents the density of occurrences within a time interval, as modeled by the Poisson distribution.

In mathematical logic and computer science, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus.

Lambda is a unit of volume, synonymous with one microliter (1 μL), that is, one cubic millimetre (1 mm3). This use is currently deprecated.

Lambda indicates an eigenvalue in the mathematics of linear algebra.

In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in coulombs per meter).

Lambda denotes a Lagrange multiplier in multi-dimensional calculus.

In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET.

In ecology, lambda denotes the long-term intrinsic growth rate of a population. This value is often calculated as the dominant eigenvalue of the age/size class matrix (mathematics).

In formal language theory and in computer science, lambda denotes the empty string.

Lambda is a nonstandard symbol in the International Phonetic Alphabet for the voiced alveolar lateral affricate [dɮ].

Lambda denotes the Lebesgue measure in mathematical set theory.

The Goodman and Kruskal's lambda in statistics indicates the proportional reduction in error when one variable's values are used to predict the values of another variable.

Lambda denotes the oxygen sensor in a vehicle that measures the air-to-fuel ratio in the exhaust gases of an internal-combustion engine.

A Lambda 4S solid-fuel rocket was used to launch Japan's first orbital satellite in 1970.[6]

Lambda denotes the failure rate of devices and systems in reliability theory, and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the mean time between failures.

In criminology, lambda denotes an individual's frequency of offenses.

In cartography and navigation, lambda denotes the longitude of a location.

In electrochemistry, lambda also denotes the ionic conductance of a given ion (the composition of the ion is generally shown as a subscript to the lambda character).

In neurobiology, lambda denotes the length constant (or exponential rate of decay) of the electric potential across the cell membrane along a length of a nerve cell's axon.

In the science and technology of heat transfer, lambda denotes the heat of vaporization per mole of material (a.k.a. its "latent heat").[7]

In the technology and science of celestial navigation, lambda denotes the longitude as opposed to the Roman letter "L", which denotes the latitude.

In 1970, a lowercase lambda was chosen by Tom Doerr as the symbol of the New York chapter of the Gay Activists Alliance.[10][11] The lambda symbol became associated with Gay Liberation[12][13] and recognized as an LGBT symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh,[14] the gay rights organization Lambda Legal, and the Lambda Literary Foundation, among others.

... How many Wikipedia articles do you just have memorized?

A lot!

[siva3155]

300+ TOP DHCP Objective Questions and Answers

DHCP Multiple choice Questions :-

1. What is the purpose of the DHCP server? A – to provide storage for email B – to translate URLs to IP addresses C – to translate IPv4 addresses to MAC addresses D – to provide an IP configuration information to hosts Answer: D 2. How is the message sent from a PC2 when is first powers on and attempts to contact the DHCP Server? A – Layer 3 unicast B – Layer 3 broadcast C – Layer 3 multicast D – Without any Layer 3 encapsulation Answer: B 3. What is the default behavior of R1 when PC1 requests service from DHCP server? A – Drop the request B – Broadcast the request to R2 and R3 C – Forward the request to R2 D – Broadcast the request to R2, R3 and ISP Answer: A 4. Refer to the exhibit. Which rule does the DHCP server use when there is an IP address conflict? A. The address is removed from the pool until the conflict is resolved. B. The address remains in the pool until the conflict is resolved. C. Only the IP detected by Gratuitous ARP is removed from the pool. D. Only the IP detected by Ping is removed from the pool. E. The IP will be shown, even after the conflict is resolved. Answer: A 5. How does a DHCP server dynamically assign IP address to host? A. Addresses are allocated after a negotiation between the server and the host to determine the length of the agreement. B. Addresses are assigned for a fixed period of time. At the end of period, a new quest for an address must be made, and another address is then assigned. C. Addresses are leased to host. A host will usually keep the same address by periodically contacting the DHCP sever to renew the lease. D. Addresses are permanently assigned so that the host uses the same address at all times. Answer: C 6.  Which two tasks does the Dynamic Host Configuration Protocol perform? (Choose two) A. Set the IP gateway to be used by the network. B. Perform host discovery used DHCPDISCOVER message. C. Configure IP address parameters from DHCP server to a host. D. Provide an easy management of layer 3 devices. E. Monitor IP performance using the DHCP server. F. Assign and renew IP address from the default pool. Answer: C F 7. Which statement is correct regarding the operation of DHCP? A. A DHCP client uses a ping to detect address conflicts. B. A DHCP server uses a gratuitous ARP to detect DHCP clients. C. A DHCP client uses a gratuitous ARP to detect a DHCP server. D. If an address conflict is detected, the address is removed from the pool and an administrator must resolve the conflict. E. If an address conflict is detected, the address is removed from the pool for an amount of time configurable by the administrator. F. If an address conflict is detected, the address is removed from the pool and will not be reused until the server is rebooted. Answer: D 8. Which statements are true about the DHCP quarantine method? (Select two.) A. The DNS server for a quarantine subnet is assigned by the enterprise DHCP server. B. A quarantine subnet consists of a set of IP addresses dynamically assigned to endpoints. C. Endpoint Integrity can be managed for endpoints with static IP addresses by defining exceptions. D. A non-quarantine IP address is assigned by the NAC 800 after an endpoint passes integrity testing. E. Port 2 of the NAC 800 can be connected to a switch that provides a path to multiple DHCP servers. Answer: BE 9. A ProCurve 3500yl switch is connected to port 1 of a ProCurve NAC 800 and a DHCP server is connected to port 2. The DHCP server IP address is 10.1.10.10/24. The NAC 800 IP address is 10.1.10.20/24. The IP address 10.1.24.1/24 is assigned to VLAN 24 on the switch. Which additional configuration settings would be appropriate for supporting a 10.1.24.0/24 non-quarantine subnet and a 10.1.25.0/24 quarantine subnet? (Select two.) A. on the switch, a multinetted IP address of 10.1.25.1/24 assigned to VLAN 24 B. on the NAC 800, the IP address of the DHCP server specified as 10.1.10.10/24 C. on the NAC 800, IP addresses 10.1.24.51 through 10.1.24.100 defined as exceptions D. on the switch, the IP helper addresses 10.1.10.10 and 10.1.10.20 defined for VLAN 24 E. on the DHCP server, one scope for 10.1.24.0/24 and a second scope for 10.1.25.0/24 Answer: AD 10. Which configuration task is applicable to the ProCurve NAC 800 inline quarantine method? A. Enable the internal firewall. B. Specify one or more quarantine subnets. C. Add IP address entries to the Accessible Services List. D. Select the port to be used for connection to the external network. E. Identify the static and DHCP IP address ranges of endpoints to monitor. Answer: C

DHCP MCQs 11. What is an important factor to consider when deploying the ProCurve NAC 800 using the DHCP quarantine method? A. The IP address lease duration must be set to five minutes or less on the DHCP server. B. The DHCP server requires one additional, non-overlapping scope for every existing DHCP scope. C. A switch must support traffic mirroring for each DHCP server protected by the NAC 800. D. Endpoint Integrity cannot be enforced for devices using static IP addresses. E. The DNS server scope option on the DHCP server must be set to the IP address of the NAC 800. Answer: D 12. A network is configured to support a ProCurve NAC 800 operating with the DHCP quarantine method. How does an endpoint transition from a quarantine IP address to a non-quarantine IP address after passing integrity testing? A. The NAC 800 triggers the switch to re-authenticate the endpoint causing a new DHCP request to be issued. B. The NAC 800 sends a DHCP release to the endpoint followed by a DHCP assignment message with the IP address. C. The switch stops forwarding DHCP requests from the endpoint to the NAC 800 and instead sends them to the DHCP server. D. Any subsequent DHCP request from the endpoint is allowed by the NAC 800 to pass to the DHCP server. Answer: D 13. A network is configured to support a ProCurve NAC 800 operating with the DHCP quarantine method. The NAC 800 is located between a ProCurve 3500yl switch and a DHCP server. How is DHCP traffic processed when an endpoint, that is currently unknown to the NAC 800, sends a DHCP request for an IP address? A. The switch requests the endpoint’s integrity state from the NAC 800 before forwarding to the DHCP server. B. If the NAC 800 receives a DHCP request addressed to the DHCP server, the request is blocked by the NAC 800. C. The DHCP server checks the endpoint’s integrity state passed to it by the NAC 800 before responding with an IP address. D. The DHCP server responds with a quarantine IP address initially and waits for the NAC 800 to indicate the endpoint has passed integrity testing. Answer: B 14. A ProCurve 5406zl switch is connected to port 1 of a ProCurve NAC 800 and a DHCP server is connected to port 2 of the NAC 800. You are planning to deploy the ProCurve NAC 800 with the DHCP quarantine method using a shared subnet approach. Which configuration requirement must be satisfied? A. The quarantine and non-quarantine subnets defined on the NAC 800 must be the same. B. The switch requires that separate VLANs be defined for the quarantine and non-quarantine subnets. C. Each switch VLAN supporting the endpoints must use a single IP helper set to the IP address of the NAC 800. D. The scope on the DHCP server and the quarantine subnet on the NAC 800 must use non-overlapping IP addresses. Answer: D 15. You are configuring a ProCurve NAC 800 to operate using the DHCP quarantine method. Which parameters are specified when adding a quarantine area? (Select three.) A. IP address of the DHCP server B. IP address of a RADIUS server C. IP address of a default gateway D. range of quarantine IP addresses E. lease duration time for IP addresses F. non-quarantine subnet using CIDR notation G. IP address of a DNS server for quarantine subnet H. static route for endpoints to use when quarantined Answer: C,D,F 16.   _____ Sets an alias for a host name A. DNS Event Logging tab B. DNS Debug Logging tab C. DNS CNAME (canonical name) Ans: C 17.    10.0.0.0 255.0.0.0 (Assignable IP range - 10.0.0.1-10.255.255.254) is A. Class C B. Class D C. Class A D. Class B Ans: C 18.  _______ : Declares the host that's the most authoritative for the zone and, as such, is the best source of DNS information for the zone. A. DNS PTR Record B. DNS Start of Authority C. DNS Monitoring tab D. DNS A Record Ans: B 19. which is the type of DNS Scopes A. Normal DHCP Scope B. Normal, Multicast, Super C. Multicast Scope D. Forward Lookup Zone Ans: B 20. _____. Is the process of placing timestamps on dynamically registered records A. Aging B. IP C. AIPAA D. TCP Ans: A 21. which IP range is  69.254.0.1 to 169.254.255.254 / 255.255.0.0 A. Aging B. TCP C. AIPAA Ans: C 22. _________ indicates that the DHCP server is authorized and active A. DHCP Server Migration B. DHCP white circle with green up arrow C. DHCP white circle with red down arrow D. DHCP red circle with X Ans: B 23. _______ DNS tab to perform basic tests of name resolution A. DNS PTR Record B. DNS Monitoring tab C. DNS Debug Logging tab D. DNS A Record Ans: B 24. Connection Oriented Protocol for end-to-end communication is called A. Aging B. CORRECT: TCP C. IP D. None of the above Ans:  B 25. DHCP audit logs are stored in ________ A. Multicast Scope B. DNS PTR Record C. Super Scope D. %systemroot%system32dchp Ans: D 26. DHCP ____ _______ occur every 60 minutes A. Multicast Scope B. Super Scope C. Subnet Mask D. Automatic Backups Ans: D 27. DHCP servers dynamically update ____________ on behalf of clients using secure updates A. DNS A Record B. Automatic Backups C. DNS PTR Record D. A & PTR Records Ans: D 28.  ________ DNS tab for detailed troubleshooting A. DNS PTR Record B. Scavenging C. DNS Event Logging tab D. DNS Debug Logging tab Ans: D 29. ______ interval is the period after the no-refresh interval during which the timestamp can be refreshed. A. Refresh Interval B. Class A C. No-refresh Interval D. DNS A Record Ans: A 30. ______ interval is the period after the timestamp is set that must elapse before refresh can occur. A. Nonsecure Method B. Refresh Interval C. Forwarder D. No-refresh Interval Ans: D 31. _____ - on server, server is not authrozied in Active Directory A. DHCP white circle with green up arrow B. DHCP white circle with red down arrow C. DHCP red circle with X D. DHCP Server Migration Ans: B 32. internetworking protocol for routing packets over a network is called_________. A. IP B. AIPAA C. TCP D. Aging Ans: A 33. ____________ scope is needed for Assigning Class A, B, C IP addresses and related network settings A. Multicast Scope B. Forward Lookup Zone C. Super Scope D. Normal DHCP Scope Ans: D 34. ______ Maps an IP address to a host name for reverse lookups A. DNS A Record B. A & PTR Records C. Super Scope D. DNS PTR Record Ans: D 35. Dynamic DNS clients register their A records using a ______ method A. DNS PTR Record B. Scavenging C. DNS A Record D. Nonsecure Method Ans: D 36.  _____ is used to determine the IP address of a computer from its FQDN A. Forward Lookup Zone B. Forwarder C. Reverse Lookup Zone D. Normal DHCP Scope Ans: A 37.  Name server designated as the recipient of forwarded queries is known as _______ A. Class B B. Class C C. Forwarder D. None of the above Ans: C 38. what is %systemroot%System32DHCP A. DHCP Server Migration B. DHCP red circle with X C. DHCP Lease 4 part process D. DHCP Database location Ans: D 39. _______ is used for assigning Class D IP addresses and related network settings A. Normal DHCP Scope B. Super Scope C. Class C D. Multicast Scope Ans: D 40. Every DHCP server must have at least one active scope to grant leases to clients A. True B. False Ans: A 41.  which Displays entries in DNS cache A. ipconfig /displaydns B. ipconfig /flushdns C. Normal DHCP Scope D. ipconfig /registerdns Ans: A 42.  _____is the process of deleting outdated (stale) resource records. A. Class A B. False C. Scavenging D. Aging Ans: C 43. _________Refreshes leased IP addresses and re-registers DNS A. ipconfig /flushdns B. ipconfig /registerdns C. DNS A Record D. ipconfig /displaydns Ans: B 44. _____ is used to determine a computer's FQDN from it's IP address A. Forward Lookup Zone B. Normal DHCP Scope C. Super Scope D. Reverse Lookup Zone Ans: D 45. _______ is used as containers for scopes A. Super Scope B. DNS PTR Record C. Multicast Scope D. Subnet Mask Ans: A 46. _____ Maps a host name to an IP address. A. DNS A Record B. Forwarder C. Super Scope D. DNS PTR Record Ans: A 47. which Identifies with parts of the IP adddress belong to the network ID and which parts belong to the host ID. A. Class A B. Subnet Mask C. Super Scope D. Scavenging Ans: B 48.  what is DHCP 044? A. DHCP options for IPv6 B. DHCP options DNS Servers C. DHCP options WINS node type D. DHCP options WINS Servers Ans: D 49. what is DHCP 003? A. DHCP options B. DHCP options for IPv6 C. DHCP options DNS Servers D. DHCP options Router Ans: D 50.  ___________netsh dhcp server scope 192.168.1.0 add exclude range 192.168.1.1 192.168.1.25 A. Server core, create DHCP reservations B. Server core, create DHCP exclusions C. Server core start the DHCP service. D. Server core, create DHCP scope. Ans: B DHCP Questions and Answers pdf Download Read the full article

[mathematicianadda]

G2D2, 2: first week

The campus of the China Three Gorges Hotel has a small river, full of waterlilies and lotus flowers. Beside it runs a main road, along which big water trucks run, shooting atomised water from cannon-like structures; we are told this is to reduce the air pollution.

After an introductory party on Monday, the conference opened at 9:00 on Tuesday morning. In the first week, much of the activity is minicourses 1 and 2, the first on “Laplacian eigenvalues and optimality” given by Rosemary and me, the second on “Topics in representation theory” by Tullio Ceccherini-Silberstein.

But first, some words on the two logos, which appear at the top of the first post in this sequence.

The meeting is being held in the Three Gorges Mathematics Research Centre, whose logo is on the right. It is part of the China Three Gorges University, near the famous Three Gorges on the Yangtse River. The University’s logo, which I am sure your search engine will quickly find, features three vertical wavy shapes, which presumably are intended to suggest water cascading through the three gorges. The TGMRC logo cleverly replaces these random shapes by integral signs, which they somewhat resemble.

The TGMRC is on a corridor on the top floor of a U-shaped building called L1 or L2, depending on which side you enter. The top of the U is closed by a high bridge. So it somewhat resembles the new location of the ICMS in Edinburgh, except that that building is entirely enclosed, whereas the central courtyard of L1/L2 is open to sun and rain. There is a nice lecture room with comfortable chairs. Although there is no public space except for the corridor (where the welcome party was held), there are a number of rooms which can be used as “breakout rooms” for small discussions.

The conference logo on the left is a Deza graph. There has been a recent upsurge of activity on Deza graphs, which I suspect is driven by Sergey Goryainov.

A Deza graph is a regular connected graph for which the number of common neighbours of two vertices takes just two distinct values. If adjacent vertices have one number of common neighbours and non-adjacent vertices the other, then the graph is strongly regular. So a strictly Deza graph is defined to be a Deza graph of diameter 2 which is not strongly regular. The graph in the G2D2 logo is the smallest strictly Deza graph, as you can easily verify. I do not know whether the colours have any mathematical significance.

On Wednesday, Dmitry Panasenko told us about a clever computer search which found all the strictly Deza graphs on up to 21 vertices. For one parameter set (I think on 20 vertices) there are many non-isomorphic graphs (I think around 20 or 30, though I didn’t copy down the number from a long table). Then Soesoe Zaw told us about some new constructions of strictly Deza graphs from the Berlekamp–van Lint��Seidel graph, using the operation of dual Seidel switching due to Willem Haemers. This pleases me, since I am typing this on a computer called Seidel.

The Berlekamp–van Lint–Seidel graph is a graph on 243 vertices which is dual (in the sense of Delsarte duality for association schemes) to the graph associated with the perfect ternary Golay code C of dimension 5 over the field of 3 elements. Take the dual code of C (which is 6-dimensional of length 11 and contains C as a subcode of codimension 1). The vertices of the graph are the cosets of this dual code; two vertices are joined if their difference contains a word of weight 1. It is a “sporadic” strongly regular graph with 243 vertices, and from it Soesoe was able to construct a strictly Deza graph on 243 vertices and two of them on 486 vertices.

Seidel’s name came up again in Wei-Hsuan Yu’s talk on equiangular lines, in which he began with the results which I saw from close-up in the early 1970s by Lemmens, Seidel, Higman, Taylor, Gerzon, and so on, and then gave some improvements, some of which have been obtained by semi-definite programming; and again in Alexander Gavrilyuk’s talk on digraphs whose Hermitian adjacency matrices have spectral radius at most 2.

One of the invited speakers was Gareth Jones. He was going to tell us about his recent theorem that many triangle groups contain uncountably many maximal nonparabolic subgroups (subgroups maximal with respect to containing no parabolic elements in their action on the hyperbolic plane). But for reasons not revealed, he was unable to come to the meeting. Instead, Alexander Mednykh had offered to give a talk to Gareth’s slides. Very brave, I thought. But Sasha began by explaining to us the basic idea behind the proof, a mix of maps and hypermaps, coverings, Riemann surfaces, etc.

Qing Xiang gave us new bounds for the size of a partial ovoid in either the generalised quadrangle E(5,q) (what I might call Ω−(6,q) and in the Ree–Tits generalised octagon; in each case, previous bounds were of order a power of q, but he and his co-authors have managed to lower the exponent of the power. He showed us Chris Godsil’s nice proof of Jef Thas’ q3−q2+q bound in the GQ case, based on association scheme techniques (and so potentially useable in much more general situations). The new bound uses modulo p techniques and very specific results about dimensions of modules for algebraic groups, and while much more powerful in this case is likely to be much more specialised.

There have been several mentions of Cayley graphs, and I must point out a notational trap. Given a subset S of a group G, not containing the identity, the Cayley (di)graph Cay(G,S) is the graph with vertex set G and with an arc from x to sx for every s in S. If S is inverse-closed, it is an undirected graph. It admits the action of G on itself by right multiplication (the right regular action) as automorphisms. In fact, any graph which admits G acting regularly as a group of automorphisms is necessarily a Cayley graph for G.

Now there are two, quite different, definitions of a normal Cayley graph:

The definition I learned first says that Cay(G,S) is a normal Cayley graph if S is a normal subset of G (closed under conjugation by elements of G); equivalently, the graph admits both the left and the right regular action of G as automorphisms.

The definition which seems to be standard among participants at this conference is: Cay(G,S) is a normal Cayley graph if G is a normal subgroup of the full automorphism group of the graph.

The first definition is very restrictive but also very useful. For two examples,

A graph invariant under the primitive group of simple diagonal type whose socle is the product of two copies of the simple group T is a normal Cayley graph for T.

For n > 3, Henson’s universal homogeneous Kn-free graph is not a normal Cayley graph for any group (though Greg Cherlin showed that it is a Cayley graph).

The second definition, by contrast, says essentially that a normal Cayley graph has no “unexpected” automorphisms: its automorphism group is contained in the holomorph of G. In accordance with the principle that graphs tend to have few automorphisms other than those you must have, we would expect that most Cayley graphs are normal; this has indeed been conjectured, with some evidence.

I wish that we had different words for these two obviously useful concepts. But it is probably too late for that now; one of them will just fade away.

The paragraph two above reminds me of an old theorem of mine, the citation for which was just imported from Scopus into the St Andrews research repository. For every finite group G, there is a constant α(G), between 0 and 1, so that, in the class of n-vertex graphs whose automorphism group contains a subgroup isomorphic to G, the proportion whose automorphism group is exactly G tends to the limit α(G) as n→∞. In accordance with the above principle, you might expect that most groups have α(G) = 1; but in fact this happens if and only if G is a direct product of symmetric groups, and the values of α are dense in the unit interval.

The idea of terminology fading away came up in Misha Muzychuk’s nice survey of coherent configurations for the summer school. As I have probably pointed out here before, at the end of the 1960s, within a couple of years of each other, Donald Higman invented coherent configurations, while Weisfeiler and Leman invented cellular algebras. The latter notation has faded away, partly because the term has been re-used with an entirely different meaning. But long before this, Bose and Nair invented association schemes, which are an important special case of coherent configurations. There are four levels of generality; in increasing generality, a coherent configuration may be symmetric, commutative, homogeneous, or none of the above. Bose and Nair used the term “association scheme” for symmetric c.c.; Delsarte used it for commutative c.c.; Bannai and Ito used it for homogeneous c.c., and this seems to have become standard. I prefer to use the term “coherent configuration” with appropriate qualification.

Unfortunately Misha did not have time to describe his recent construction, with Klin and Reichard, of proper Jordan schemes; but Mike Kagan will talk later in the meeting, and I think he might say something about this.

from Peter Cameron's Blog https://ift.tt/2KHbSWq from Blogger https://ift.tt/2YVjXzn

[inordi]

Adding Tetrads

An exhibition of tumblr's mathematical markdown

We have, in dodecaphony, four all-interval1 tetrads represented by the four polynomials $$p_1(x) = 1+x+x^3+x^7$$ $$p_2(x) = 1+x+x^4+x^6$$ $$p_3(x) \cong p_1(x^{-1}) \equiv 1+x^4+x^6+x^7$$ $$p_4(x) \cong p_2(x^{-1}) \equiv 1+x^2+x^5+x^6$$

Some may better know these as, respectively, PC Sets 4-Z29A, 4-Z15A, 4-Z29B and 4-Z15B in the Fortean nomenclature.

Each may add a transposition of one of the others to form an octad. For example we may add 4 semitones to the second (thus producing the non-interfering tetrad $x^4+x^5+x^8+x^{10}$) and add this to the first to produce

$$p_1(x) + x^4 p_2(x) = 1 + x + x^3 + x^4 + x^5 + x^7 + x^8 + x^{10}$$

The tetrad addition is valid only when the two pitch class sets being 'added' have no pitch classes in common. Due to that limitation, it turns out that - of the 66 ways we may calculate $p_i(x) + x^k p_j(x)$ (where $0 \lt k \lt 12$ and $1 \leq i \lt j \leq 4$) there are only 14 possible octads:

$$q_1(x) = p_1(x) + x^4 p_2(x)$$ $$q_2(x) = p_1(x) + x^5 p_2(x)$$ $$q_3(x) = p_1(x) + x^{10} p_2(x)$$ $$q_4(x) = p_1(x) + x^2 p_3(x)$$ $$q_5(x) = p_1(x) + x^4 p_3(x)$$ $$q_6(x) = p_1(x) + x^{10} p_3(x)$$ $$q_7(x) = p_1(x) + x^4 p_4(x)$$ $$q_8(x) = p_2(x) + x^2 p_3(x)$$ $$q_9(x) = p_2(x) + x^3 p_4(x)$$ $$q_{10}(x) = p_2(x) + x^5 p_4(x)$$ $$q_{11}(x) = p_2(x) + x^9 p_4(x)$$ $$q_{12}(x) = p_3(x) + x^3 p_4(x)$$ $$q_{13}(x) = p_3(x) + x^8 p_4(x)$$ $$q_{14}(x) = p_3(x) + x^9 p_4(x)$$

where all multiplications are performed modulo $(x^{12}-1)$, i.e. by taking remainders after polynomial division by $(x^{12}-1)$2.

Now both $q_7(x)$ and $q_8(x)$ turn out to be the fairly well known 'octatonic scale' constructed by four consecutive semitone+wholetone steps. Note that $q_7$ combines $p_1$ with $p_4$ - i.e. $p_1$ to $p_2$'s (transposed) inversion whereas $q_8$ combines $p_2$ and $p_1$'s (transposed) inversion.

Due to similar relationships, the 14 octads turn out to be congruences3 of only 7 distinct octads, all of them being symmetric (i.e. inversionally identical). In prime form they are:

$$o_1(x) = 1 + x + x^3 + x^4 + x^6 + x^7 + x^9 + x^{10}$$ $$o_2(x) = 1 + x + x^2 + x^4 + x^6 + x^7 + x^8 + x^{10}$$ $$o_3(x) = 1 + x + x^3 + x^4 + x^5 + x^7 + x^8 + x^{10}$$ $$o_4(x) = 1 + x + x^2 + x^3 + x^6 + x^7 + x^8 + x^9$$ $$o_5(x) = 1 + x + x^3 + x^4 + x^5 + x^6 + x^8 + x^9$$ $$o_6(x) = 1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^9$$ $$o_7(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^9$$

which are the Fortean PC Sets known as 8-28, 8-25, 8-26, 8-9, 8-17, 8-10, 8-3.

The $q_i(x)$ may then be expressed in terms of these:

$$q_2(x) = x^{-1} q_{13}(x),~where~q_{13}(x) \cong o_2(x)$$ $$q_3(x) = x^{-5} q_{12}(x),~where~q_{12}(x) \cong x^{3} o_7(x)$$ $$q_5(x) = x^{-5} q_9(x),~where~q_9(x) \cong o_5(x)$$ $$q_7(x) = q_8(x),~where~q_8(x) \cong o_1(x)$$ $$q_{10}(x) = x^{-2} q_4(x),~where~q_4(x) \cong o_4(x)$$ $$q_{11}(x) = x^{-1} q_6(x),~where~q_6(x) \cong x^{-2} o_6(x)$$ $$q_{14}(x) = x^{-1} q_1(x),~where~q_1(x) \cong o_3(x)$$

An application of this particular 'tetradic addition' would be the addition of $p_1(x)$ rendered as the set of pitches C, C#, E♭, G and the set $p_2(x)$ rendered as C, C#, E, F# transposed (by the $x^4$ multiplication) four semitones up to E, F, A♭, B♭. This produces the eight pitches (in order) as C, C#, E♭, E, F, G, A♭, B♭ (corresponding to pitch classes 0, 1, 3, 4, 5, 7, 8, 10 as per the polynomial).

Forte-wise, this might be expressed as something like 8-26 = 4-Z29A + 4-Z15A.T4, where the .T4 operator applied to a PC set indicates its transposition by four semitones.

The image above shows the seven distinct constructions in an arrangement where the prime-form 4-29A is fixed (as $p_1(x) = 1+x+x^3+x^7$, if you will) at the top of a 'pitch class clock'. Addends and sums are oriented appropriately with respect to it. Each tetrad pair (in pink, indicating their inherent inversional asymmetry) is in one clock and its summed octad (blue, indicating inversional symmetry) is in its own clock to its right. Labels are Fortean PC Set names located at PC element 0 positions. Consequently some may almost be upside down.

So a second example of such a 'Fortean operational notation' is demonstrated by 8-25's '11 o'clock' orientation showing the image 8-25.TB = 4-Z29A + 4-Z15A.T5 (where .TB is a transposition 11 semitones clockwise, or 1 anticlockwise). Shifting this expression clockwise 1 semitone (to 'right' the 8-25) would require an application of .T1, and, bearing in mind that .TB.T1 $\equiv$ .T0 is effectively a no-op, the expression would end up as 8-25 = 4-Z29A.T1 + 4-Z15A.T6 (as the operational composition .T5.T1 is, of course, .T6). This is the same as:

$$1+x+x^2+x^4+x^6+x^7+x^8+x^{10} = x(1+x+x^3+x^7) + x^6(1+x+x^4+x^6)$$ $$ = x+x^2+x^4+x^8+x^6+x^7+x^{10}+x^{12}$$

where the equality holds because $x^{12} mod (x^{12}-1) \equiv 1.$4

You may satisfy yourself (or not) that these correspond exactly with polynomial representations where the .T$n$ operation corresponds to polynomial multiplication by $x^n$ (results taken modulo $(x^{12}-1)$).

Thus polynomial representations of pitch class sets (and its operational arithmetic) are extremely useful for the compact linearity of text. Not to mention avoiding the need to name PC sets. Pictorial representations are possibly clearer, but of course they take up more real-estate.

An all-interval tetrad contains one of each non-trivial dodecaphonic interval $1 \dots 11$, where $p_i(x) p_i(x^{-1}) = 4 + x + x^2 + x^3 + x^4 + x^5 + 2 x^6 + x^7 + x^8 + x^9 + x^{10} + x^{11}$ - all multiplications taken modulo $(x^{12}-1)$. In terms of the six interval classes $|i|$, this is the same thing as $4 + 2(x^{|1|}+x^{|2|}+x^{|3|}+x^{|4|}+x^{|5|}+x^{|6|})$. ↩︎

Note that there's no point in attempting to find other additions $p_i(x) + x^k p_j(x)$ where $j \lt i$ since $p_j(x) + x^{-k} p_i(x)$ is the same octad as $p_i(x) + x^k p_j(x)$ transposed $k$ steps down. ↩︎

Congruence of pitch class sets means that they are - at most - only 'modally' distinguishable, i.e. that one may be rotated directly onto another. Since all these octad sets are also inversionally equivalent, the additional issue of reflectional equivalence does not arise. ↩︎

In general, $x^{12+n}~mod(x^{12}-1) \equiv x^n$ for all $n \ge 0$. This is because in order to (polynomially) divide $x^{12+n}$ exactly by $x^{12}-1$ you must first subtract $x^n$ (to get $x^{12+n}-x^n=x^n(x^{12}-1)$, exactly divisible by $x^{12}-1$, resulting in $x^n$ which is ignored) and add it back on again afterwards as the remainder, which is the modulo result you need - provided, of course, that $n \lt 12$ (if not, then rinse, repeat etc as usual for modulo arithmetic). ↩︎

[t-baba]

New ES2018 features worth knowing (with examples)

#419 — January 11, 2019

Read on the Web

JavaScript Weekly

FromJS: An Experimental Data-Flow Analysis Tool for Front-End JS — An interesting tool that shows you where each value in the DOM comes from - very useful for looking at how other pages work or for certain types of debugging. There’s also a blog post and video about how it works. Note: Requires Node 9 or under for now.

Matt Zeunert

New ES2018 Features Every JavaScript Developer Should Know — ES2018 wasn’t as huge a leap forward as ES6, but this post is packed with interesting examples of spread properties within object literals, asynchronous iterators and asynchronous iterables, Promise.prototype.finally, and other new features.

Faraz Kelhini

Frontiers 2019: Explore New Ways to Build Apps on Slack — Frontiers is a Slack conference exploring the future of work. In the developer track, you'll get immersive training on new functionality and hands-on workshops for app builders at all development stages. Register today for early bird pricing.

Slack sponsor

Node and JavaScript Testing Best Practices — A well presented collection of 30 best practices for better JavaScript testing, continuous integration, and overall quality.

Yoni Goldberg

2018 JavaScript Rising Stars — An annual roundup of which JavaScript projects did well in terms of GitHub stars over the prior year in various categories. It’s a bit of a popularity contest but it’s nice to get a feel for what’s going on.

Michael Rambeau

Anime.js 3.0: A JS Animation Library for the Web — A mature and powerful animation library takes another step forward with a new site, new documentation and examples, new easings, new callbacks, and more.

Julian Garnier

GitHub Announces Unlimited Free Private Repos — A late Christmas present comes from GitHub in the shape of their free offering now including unlimited private repositories (something that previously cost $7/mo) with a limit of three collaborators per repo. For balance, GitLab’s CEO had a response.

GitHub

💻 Jobs

Senior Web Developer at Dr. Bill (Remote OK) — Dr. Bill helps Canadian doctors save time by streamlining their billing. Help lead our team into the next phase of growth.

Dr. Bill

JavaScript/Node Developer - Brighton UK — Growing new-product team, modern JavaScript tools and data-driven innovation. Flexible working and a fierce commitment to L&D.

Madgex

Find A Job Through Vettery — Vettery matches top tech talent with growing companies. Create your profile to get started.

Vettery

📘 News, Tutorials and Opinions

Defensive JavaScript — “How to write code that doesn’t do what it oughtn’t”

Mike Samuel (Google)

How Do Top Developers Deliver Video? - Download the 2018 Video Report — Hundreds of developers around the world reveal their preferred video streaming solutions.

Bitmovin sponsor

Setting a React Project From Scratch Using Babel and Webpack

Anshul Goyal

A Look at TypeScript 2.8's Conditional Types — An intro to conditional types, a powerful addition to the type system introduced in TypeScript 2.8.

Marius Schulz

10 Best Tips for Learning Vue from Vue Masters — 6 Vue experts talk about what they wish they would have known when first starting out.

Gregg Pollack

So Many Ways to Learn Kotlin - Which Is Right for You?

Big Nerd Ranch sponsor

Things Dan Abramov Doesn’t Know — React core team member and the creator of Redux wants you to realize that “even your favorite developers may not know many things that you know” and shares his own list of blind spots.

Dan Abramov

Aurelia 2018 Year in Review — Not just a look back but a look at what’s happening this year too with the component-oriented client framework.

Rob Eisenberg

🔧 Code and Tools

DoneJS 3 Released — DoneJS is a framework for building high performance, real-time web and mobile apps and version 3 aims to provide ‘best in class server-side rendering’.

Matthew Phillips

Libraries To Help You Work with WebGL — Working with WebGL directly can get very verbose and technical quickly, but luckily there are libraries and toolkits to make it easier.

Arek Nawo

A Much Faster Way to Debug Code Than with Breakpoints or console.log — Wallaby catches errors in your tests and displays the results of expressions right in your editor as you type.

Wallaby.js sponsor

music-fns: Music Notation-Related JavaScript Functions — For things like working with note names, octaves, frequency, intervals, and scales.

madewithlove

Karin: A Promise Based HTTP Client That Uses Template Literals — Currently an experiment/work in progress. Uses the Fetch API under the hood.

Vahe

HotKeys.js: A Robust Library for Capturing Keyboard Input

Kenny Wong

Vue Glide: A Vue Component for the Glide.js Slider/Carousel

Anton Reshetov

by via JavaScript Weekly http://bit.ly/2FrSdaC

[ashishkumarletslearn]

Free education is the right of every student. Ashish Kumar – Let’s Learn is providing deep and detailed explanations of full syllabus, all important questions, all important examples and all NCERT solutions for Class 11 Maths through videos on YouTube Channel as well as Blogs and PDFs on website.

Students can learn through videos and blogs and can ask their doubts on Website’s Discussion panel or on YouTube’s Comments Page. Students will also be provided notes, assignments, books and various other educational resources in electronic forms like PDFs, Docs, mp4 etc., which will help them to prepare for CBSE Class 12 Board Exams but more importantly for their upcoming life’s adventures.

You can easily access all chapters with NCERT Solutions for class 11 maths on this page:  https://www.ashishkumarletslearn.com/cbse/class-11/maths/

Following are summaries of chapter wise syllabus recommended by CBSE for Class 11 mathematics students with their YouTube as well as Website links.

Unit-I: Sets and Functions

1. Sets: 

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

2. Relations & Functions:

Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions:

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type siny = sina, cosy = cosa and tany = tana.

Unit-II: Algebra

4. Principle of Mathematical Induction:

Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

5. Complex Numbers and Quadratic Equations:

Need for complex numbers, especially √ , to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.

6. Linear Inequalities:

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.

7. Permutations and Combinations:

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for and and their connections, simple applications.

8. Binomial Theorem:

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

9. Sequence and Series:

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums.

Unit-III: Coordinate Geometry

10. Straight Lines:

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slope intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

Unit-IV: Calculus

13. Limits and Derivatives:

Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

[sweetturtleharmony-blog]

Calendar 2018 Printable Free

The principles of this Maya calendar are all predicated up on a method Which was in popular usage across the spot, dating back to the fifth century BCE. It shares several facets with August 2018 printable calendar templates calendars utilized with additional sooner Mesoamerican civilizations, like the Zapotec along with Olmec and modern day or after ones like the Mixtec along with Aztec calendars.

 From the Maya Mythological convention, as recorded from Colonial Yucatec reports and rebuilt in 2018 year August Classic and Postclassic inscriptions, the deity Itzamna is often credited to attracting the wisdom of the calendar technique into the ancestral Maya, together side composing in-general and also other significant elements of Maya civilization

 The Maya calendar Is Made up of many bicycles or counts Of distinct spans. Even the 260-day calendar August 2018 year depend is called scholars because the Tzolkin, '' or Tzolk'at . The Calendar Round continues to be in use by lots of classes from the Guatemalan highlands.

 A distinct calendar has been utilized to monitor longer intervals of Time and to its inscription of all calendar dates (i.e., differentiating if a incident happened in connection with the others ). Here really is actually the Lengthy Rely . It's actually a count of times as a mythical startingpoint. [7] As stated by this correlation involving the Extended discussion and Western calendars approved from the vast bulk of Maya investigators (called the Goodman-Martinez-Thompson, or even GMT, significance ), that starting-point is equal to August 11, 3114 BCE from the proleptic August calendar Gregorian calendar or even September 6, respectively at the Julian calendar (−3113 Unusual ). The GMT correlation has been decided on by John Eric Sydney Thompson at 1935 about based on sooner correlations from Joseph Goodman at 1905 (August 1-1 ), Juan Martínez Hernández at 1926 (August 1 2 ) and Thompson himself at 1927 (August 1-3 ). [8] With its inherent character, the lengthy discussion has been able to be expanded to make reference to some date into the future or past. This calendar included using the positional notation platform, at which every single placement represented a growing a number of of the amount of times. Even the Maya numeral technique was in essence vigesimal (i.e.,'' foundation -20) and just about every device of the particular position re-presented 20 instances that the August calendar 2018 excel machine from this place which reprinted it. A major exclusion has been designed for its second-order Place-value, that as an alternative symbolized 18 × 20, or 360 times, much more closely approximating the solar yr compared to could 20 × 20 = four hundred times. The bicycles of this lengthy parade are separate of this year.

[giveuselife-blog]

Death of an Automobile Car Dealership

New Post has been published on https://giveuselife.org/death-of-an-automobile-car-dealership/

Death of an Automobile Car Dealership

Last a store calls for the giant attempt and attention and the gadgets listed under, in no precise order, are minimum considerations when terminating a franchise and Remaining a dealership operation.

THIS Checklist Isn’t “ALL INCLUSIVE”. YOU Have to Consult with YOUR Attorney AND ACCOUNTANT AND THIS Listing Ought to BE Considered AS An extra Useful resource With a view to USE TO Build UPON When you Consult with THEM.

Basic Training

1. Officers, Directors, and Shareholders

Be sure to preserve each Administrator and shareholders meetings and to obtain resolutions from each entity, authorizing the supplier to liquidate the dealership or a considerable portion of the dealership’s property.

Determine whether or not or no longer the board and shareholders may authorize you a termination bonus and prepay your in your services in “winding down the enterprise”. Consult with your accountant and Lawyer to Decide what could be a reasonable amount of compensation in the event an organization creditor challenges the transaction.

Decide if it’s miles reasonable for Officials to shop for themselves and their partner automobiles. Pay “Net” “Internet”, as that could be the sales rate if the car has been lower back to the factory or sold to a patron of the commercial enterprise.

The Officers Should open a brand new financial institution account, at a exclusive financial institution, and: (a) use a PO Box, or Non-public Mail Provider as a mailing cope with; and (b) use a exclusive test color to be able to easily Decide pre and put up Remaining assessments written.

Authorize payment to and pre-pay the enterprise’s Lawyer and accountant with a retainer. Their offerings will be needed to properly near the business and the employer won’t be able to pay them later.

Authorize pre-price of something offerings or resources the organization will need to be serviced throughout the wind-down duration. For instance, assets and private coverage, real property taxes (if the belongings Isn’t owned by means of a 3rd birthday celebration), hire, utilities and such.

2. The power and insurance

A one-sheet precis of the hire Have to be connected to the unique, so that you can facilitate subjects. The summary Must encompass such items as: the dates of the base term; the bottom hire; the modern-day hire; the dates of any option intervals, collectively with notations regarding hire will increase; The facility ownership; the lessee and lessor; a notation as to whether or not or no longer the factory has factor, or site safety; the hire as an equal to the greenback price consistent with new unit sold; and, a notation as to whether or not OR not THE lease IS ASSIGNABLE and under what situations.

Different issues regarding The ability rent consist of violations of the ADA, dangerous substances (underground gas tanks, or underground oil disposal tanks) being placed on the belongings.

Owned Facilities

With respect to receiving “manufacturing unit termination help”, a few sales and Carrier Agreements, Widespread Cars, For instance, make a difference among “proprietor occupied” and “leased” dealership Centers. Be sure to study your sales and Service Agreement as a way to recognize and be capable of capitalizing on the distinctions.

Leased Facilities

If the selling dealer’s rent element prior to the sale of the dealership is inside manufacturing unit recommendations the factory Have to make the provider’s rent payments for the duration designated inside the Carrier and income Settlement. (See, however, the EPA phase.)

check together with your insurance agent to Determine the necessities for insuring an empty constructing.

Different coverage

Further to facility coverage, the dealer will want a “tail” or rider on his or her garage keepers insurance. Most coverage these days is “claims made” versus “incidence”.

In the real exercise, Maximum cases which can be settled are settled within the coverage limits and the coverage corporation may have paid for each the protection and the agreement.

With appreciate to Medical health insurance, set up for COBRA all employees of the organization. Again, Officials and Administrators may be capable of include Medical health insurance bills as part of their wind-down reimbursement.

three. UCC, Mechanic’s Lien and Title Searches

Maximum sellers are not cognizant of all present liens on dealership’s assets.

for you to appropriately estimate the selling supplier’s predicted Net proceeds, all of these lines will need to be discovered, ideally, previous to negotiations.

Possession of Name reviews and UCC-1 reports will deliver the dealer ok time to cope with the problems and to have effortlessly to be had solutions, if and whilst a potential patron raises the issue.

four. Taxes Due and expected

The dealership’s comptroller or accountant, Should put together a sheet of all taxes currently owed through the dealership and all anticipated taxes. The List Need to pick out the quantity, to who owned and the reason. In certain states unpaid taxes have a “super lien” reputation and if unpaid the selling dealer’s assets can and can be connected to get better unpaid taxes due through the selling dealership. This attachment can occur months after the dealership has closed.

As a General rule, all people authorized to join up the bank account may be held individually answerable for at the least ½ of the payroll withholding tax, in addition to one hundred% of all of the income taxes due. Similarly, in sometimes dealers have been held in my opinion chargeable for monies gathered from customers that Ought to have been treated as “accept as true with” monies, which includes: client alternate payoffs, customer credit and existence coverage premiums, and consumer assurance and Service agreement charges.

five. Notes and Debts Receivable From Others

The “Notes and Debts Receivable – Different” account is usually a “catch-all” account at the dealership announcement. For purposes of a dealership sale, this account Should be purified (1) with the intention to apprise the dealer of any greater funds, which can be available for very last income and belongings taxes and (2) to make both the dealer and accountant aware about any “in-house” loans to Officials, Administrators and personnel, which may should be repaid.

6. Pay as you go Prices

The Prepaid cost account is any other “catch-all” account that need to be purified. whilst scheduling the Prepaid fee account the comptroller Must make a radical look for all rent and settlement deposits. Normally, Provider system on hire, cars on hire, computer systems on hire, and Different rentals made to the dealership carry protection deposits, or the final month’s price, or both.

7. Dealership employees

Together with the everyday employer-worker family members, there are very crucial prison regions which could affect Car sellers: (a) pension fund liability; and (b) kingdom and federal legal guidelines concerning closings.

In a few states, the selling supplier may be in my opinion answerable for investment employee pension budget; while in others the provider has to give personnel improve observe of any Remaining. Additionally, the united states Congress exceeded law concerning “closings”. inside the times of “closings”, each kingdom and federal legal guidelines put a minimal on the quantity of individuals employed, normally 50 or a hundred, before the regulation applies to the dealer’s company. test the Hart Scott Rodino Act (HSR) and the WARN Act.

With recognize to wages, some jurisdictions have enacted statutes making positive shareholders for my part responsible for company debts because of employees and Other employees. Welfare and pension budget Also qualify as wages under Big apple’s statute.

The comptroller or accountant Ought to put together a Listing of these liabilities, to include any quantities due to the personnel, with recognizing to accrued vacations, withholding taxes, pension and profit sharing plans and wages, as of the date of close.

Insofar because the real terminations are concerned, if the dealership is “union”, the supplier Need to communicate to the union’s consultant in order to make sure that all of the conditions of the union settlement are met.

eight. Long-term Debt

All lengthy-term debt Should be itemized and a technique of repayment determined. Hobby Must be computed. when overdue Hobby and past due bills are brought to the mortgage stability, the mortgage pay-offs are generally better than anticipated.

The comptroller Should prepare a List of those money owed, to encompass the amount owed which include Hobby, to who owed, cause of debt, adulthood, phrases and safety given. In addition, after the List is finished, the comptroller Should keep a strolling overall, every day, via near of escrow.

9. Different Notes Payable

As with lengthy-term debt, Other notes payable Need to be indexed by amount including Hobby to date of near, to whom owed, purpose of word, adulthood, terms and protection given; and preparations Have to be made to retire the debt.

10. The Economic Statements

The retail Vehicle enterprise is one of the few organizations requiring a complete Remaining of all books and statistics, right away, at the end of every and every month. Factories and finance organizations require reporting on factory originated, or accepted forms.

In getting ready the shop for Last, a reconciliation announcement may be used, explaining classes inclusive of “Other earnings & rate”, assurance, finance and coverage income no longer shown at the statement, At the side of high-quality items.

You may want a very last Financial declaration for tax functions.

11. Garage of information

Dealerships amass a awesome deal of office work, the secure, accessible, Storage of with a view to present a vital hassle to the promoting supplier. No dealership record will be as vital as it is the day it can not be determined. Former dealers have related testimonies of attempting to retrieve files from mini-Garage Facilities, in both rain and snow.

The appropriate time period Ought to be determined, best after the dealer’s accountant and Legal professional have Taken into consideration and counseled the dealer with appreciate to statute of limitations issues and Different record retention guidelines, odd to the political vicinity wherein dealership is positioned.

12. In-house Service Contracts

If the supplier has offered any “in-house Provider contracts”, the promoting provider will now not need former customers calling at his or her domestic for upkeep, or lawsuits; therefore, a machine of Provider, alongside the following strains, Have to be negotiated with a supplier placed in near proximity to the Final keep.

13. The Tough belongings

Parts and Add-ons

every manufacturing unit has its own definition of “returnable” Parts and returnable Accessories. Maximum Additionally include a reduction for packing and transport.

Simply prior to Remaining, a PC printout ought to be received list all Parts and Add-ons, their purchase date and fee in the bill.

Elements and Accessories need to be segregated into “returnable” and “non-returnable” categories. Returnable Elements and Add-ons need to be inventoried and packaged in keeping with the manufacturing facility’s specifications

Non-returnable items need to be marketed to Other dealers or Elements houses which include “Napa”. word: a few “non-returnable” Parts can also, in fact, be returnable to the dealer from who it become bought, which includes Delco, Motorcraft, Mopar, Napa, and many others.

Do no longer mark on or harm unique applications when inventorying or packing as some factories will now not classify objects in marked packages as “returnable”.

Make certain to account for aftermarket items together with gasoline, Oil & Grease, Nuts, Bolts, materials, Work in Procedure and Restore Order (need to collect A/Rs), Symptoms, Gear, Miscellaneous system & materials.

Furniture, Furniture, and gadget

The Tough property falls into categories: (a) The ones repurchased by using the manufacturing facility, consisting of special Tools, Components equipment, Signs and symptoms, a few laptop structures, etc.; and those no longer repurchased via the factory, which includes desks, chairs, and so forth.

Repurchased and non-repurchased items Should be segregated and an inventory / public sale Service contacted to bid the auction at the non-repurchased items. when considering the auction, phrases inclusive of advertising time, place, minimal bids, guaranteed minimums from the auctioneer, and so forth, need to be Considered.

Leasehold Enhancements

The fee of Leasehold Improvements is generally lost within the termination Procedure.

motors

whilst engaging in a new automobile inventory valuation is a fairly, habitual count, it’s also time consuming; consequently, so as for a dealer to comprehend full value, or every vehicle, at time of switch, a Checklist ought to be compiled and maintained. There are certain additions to, and subtractions from, the bill fee that should be made.

The distinction in cash to be paid via customer’s floors entity to the provider’s floors group can be enormous, in particular with appreciate to domestic traces, wherein holdback monies robotically common among $400 and $six hundred according to a unit, or extra.

A dealer needs to be privy to this determine, early on so that you can offer for the contingency in the course of negotiations.

Diverse states have laws greater liberal than the factory’s sales and Service Agreements and the particular laws of the terminating supplier’s jurisdiction Need to be the review. As an example, Maine calls for that the manufacturing unit repurchase terminating dealers’ entire new automobile car dealership inventory, regardless of version 12 months. a few states require the factory repurchase simplest present day version year cars and others present day plus three hundred and sixty-five days deliver-over.

In MSO states, the dealer Have to manage all automobile keys and MSOs – if the lender does not already have them.

put together to liquidate used motors and any dealership automobiles which include Elements vans, courtesy vehicles, demonstrators and snow plows. it is usually easier to achieve a great rate for them by means of not letting anybody “cherry pick out”. Several wholesalers Have to bid them as a “group”.

Make List of carryovers and if the manufacturing facility will no longer repurchase them have the wholesalers bid them one at a time and Also shop them with Other dealers.

dealer plates need to be surrendered and accounted for while the dealer license is terminated.

13. Value determinations and Auctions

There are a number of equipped, recognized appraisers, our company could advise. so that it will maximize the greenback cost of an appraisal or public sale, the supplier Must touch Numerous firms, Determine how they operate, what information will be required, the approach for valuing. After acquiring such facts, the dealer Need to recognize an appropriate form and schedules vital which will maximize the appraisal or sale of the constant property. Similarly, by means of assigning an employee to thoroughly prepare the assets and schedules, the provider will higher recognize the fee of the belongings on the premises.

Possibly the best issues, with appreciate to Appraisals and auctions, are: (1) neither birthday party takes the time to apprehend the techniques and reasoning utilized by the appraisal/auction employer; and (2) the dealer nearly by no means appropriately prepares the belongings and schedules. We perpetually locate that every one of the dealership’s property do not appear on schedules, both because they were completely depreciated, or due to an error.

14. Contracts for services

Carrier protection contracts and private Provider contracts Should be reviewed for private guarantees, time period and assignability. An oversight ought to mean that private liability, for overall performance, could remain with the selling provider. Provider upkeep contracts Need to be scheduled, with the element indicating the quantity of every price, length of Settlement, Carrier to be rendered, and any personal liability. Any contracts that can be cancelled Ought to be calendared for cancellation.

15. Contingent liability and Reserves

The supplier Need to understand the quantity of all extraordinary retail paper, which has been unconditionally assured through the dealership, or the supplier. The dealer Need to understand which the dealership’s reserve account will be difficult to rate backs, for early payoffs and the quantity, if any, of recourse against the supplier and the dealership.

A spreadsheet of the great contracts Have to be compiled, detailing, In addition to the collateral description, final time period and delinquency reputation, and credit score grade, including A, B, or C, or whatever system the finance business enterprise makes use of. The kind of recourse, average monthly reserve feedbacks, and the modern-day reserve stability Need to Also be covered.

Shortly after informing the financing institutions of the dealer’s motive to close the dealership, the lenders Should Again be approached, concerning the provision of any “stroll-away” packages. Moreover, inside the event the dealership has been operating with reduced reserve retention, the amount required to carry the reserve(s) to standard, upon cessation of retail operations, Should be determined. Every so often, this amount has proved to be big.

Ultimately, when confidentiality is not a problem, the dealer Have to speak with the lender, the handling of future repossessions, extensions, renewals and Other maintenance capabilities. If the earlier supplier-lender dating was true, the provider will find out that an high-quality amount of assist to be had from a cooperative finance enterprise.

Ultimately, if the supplier discovers a huge contingency, a positive diploma of assistance can be negotiated with the buyer.

16. Debts Receivable and coins

coins

at the same time as reputedly apparent, dealership cash ought to be Taken into consideration. normally a brand new bank account Should be opened at a Financial group that Is not affiliated with the provider’s present day business. Also, if feasible, a locally owned bank Need to be used, versus a countrywide bank. The supplier Need to do not forget reducing the number of signatories on the checking account(s) to 2, one among that is the dealer and, effective the day of the near, the range of signatories Should be reduced to the supplier main most effective.

manufacturing unit Receivables

From the instant a choice to close the shop is reached, manufacturing unit receivables Have to get hold of focused attention. The very instant and recognition of the pending Ultimate reaches the manufacturing facility, the bills stop.

Try to remedy all trouble receivables, which include guaranteed disputes, well earlier than the Ultimate. In any occasion, assistance from the factory, following the close of escrow could be crucial to Technique assurance re-submissions and Other issues.

employee Receivables

employee receivables Need to Additionally be thoroughly analyzed at some stage in this initial degree. An immediate policy, of no advances, Have to be installed.

Without causing alarm, worker receivables Should be scheduled and a route of repayment hooked up. one of the higher techniques is to prepare a time table of what each worker owes and, because the very last pay intervals technique, make sure the receivables are deducted from the employee’s very last tests. Alas, a few states do no longer allow the supplier to set-off debts towards wages. Your kingdom’s coverage/regulation Must be reviewed with your Legal professional before proceeding to set-off any worker debt.

client and car Receivables

The selling supplier Need to make sure that car receivables and customer Accounts, apart from Carrier and Parts, are natural. important adjustments and write-offs Ought to be made, with the motive of arriving at a receivable determine which realistically depicts the amount of cash which can be anticipated.

If the dealership’s Carrier and Parts policy has been properly monitored, these Debts Need to pay in an orderly manner. In addition, the supplier Need to decide whether or not collections Need to be achieved through dealer, and one or extra personnel, or whether or not the provider can promote the Bills to a factoring residence.

17. Leased gadget

not all leases may be cancelled. The supplier Must Determine which, if any, of the leases have non-public ensures, and with respect to such leases, make a concerted effort to negotiate a settlement with the lessor. That assumes that the business enterprise is bankrupt. If the organization is solvent, than settlements want to be negotiated with appreciate to corporate leases.

18. EPA Inspection

If the real assets is owned by means of the Last supplier, it’s miles essential for the dealer to Decide in which and what the troubles are possibly to be. If underground gas or oil Garage tanks have ever been located at the dealership actual belongings, the supplier Must, if now not already to be had, contact a Non-public inspection corporation and acquire a certificates of clearance, or compliance, with admire to it.

Be conscious, no agreements among the parties can modify, or redistribute their respective liabilities, with respect to kingdom and federal legal guidelines.

19. Expenses of Transaction

There are certain excellent Charges, consisting of actual estate appraisal expenses, representative prices, Attorney and accounting expenses, that are incidental to the getting ready a dealership for Ultimate. those Expenses will be paid each from the dealership Trendy account and without delay from the Ultimate dealer’s private account. The provider Have to alert the bookkeeper to preserve a separate journal, wherein to report these Charges, just so the accountants can also without problems Determine the prices of sale and categories of costs, for profits tax purposes, each non-public and enterprise.

Last Date

Absent exigent occasions, the provider Must estimate the quantity of time essential to prepare the shop for Closing, typically about thirty days. If possible, the Ultimate Ought to be on a payday.

The Comptroller’s Duties

The supplier’s comptroller Ought to put together, or be answerable for the Guidance of, the following gadgets and files, for switch:

The Books & facts;

All buy Orders and Deposits;

The Franchise Termination Letter and the factory’s, or Distributor’s Acceptance of the consumer’s Resignation;

The Debts Receivable Listing;

Pay as you go Prices;

getting ready a Leased device inventory;

Securing Antique credit score card plates and Machines;

The Elements and Add-ons Return, vehicle Return, and hire assistance Call for Letters;

The switch and/or cancellation of Various: Telephone Numbers; put up Office Bins;

The coverage arrangements: life, storage keeper’s tail, actual and personal assets, health, and many others.

The provider’s Responsibilities

The provider Should put together, or be accountable for reviewing and supervising all the items within the Tick-list and for the Education of the following objects:

determine at the employees which might be required to live in order to finish the Remaining of the store.

check for offered orders determines whether or not to supply, cancel, or check with every other provider.

Cancel corporation credit playing cards, such as any smartphone credit cards and any cellular phones – except your very own.

At ease Phone Service. Set a Voice Mail message concerning a dealership referral.

Determine THE factory’S Obligations WITH appreciate TO ITS RIGHTS TO hire AND buy. Be sure TO MAKE CLAIMS AND REQUESTS FOR help inside the term distinct within the sales AND Provider Agreement.

If vital, communicate to a Realtor and Listing The power on the market (rent or sale).

Discover in which credit score card monies are deposited and circulate the account if it’s far inside the same bank wherein the corporation’s Well known account is living.

near out, or switch to every other dealer all energetic Provider ROs. If viable, negotiate a referral charge.

Create a press launch for keep Final.

Cancel all new vehicle orders that aren’t scheduled, do no longer order any new automobiles.

close out all Carrier ROs in order that Paintings is finished by using the date of near. Do now not accept any Work that cannot be completed with the aid of keep shutdown date.

As usually, when Final a dealership, you Ought to continually Consult with a certified Lawyer and accountant.