#cartesian components

[er-cryptid]

Polar to Cartesian Components [Ex. 1]

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[huayno]

the term "invalidate" acknowledges that emotions have reasons as components, while simultaneously insisting that emotion be left in a protected domain instead of evaluated on that basis. basically a separate spheres/hostile worlds ideology for what cartesian dualism takes as a given. being dogmatically against emotional invalidation results in things like NVC proscribing telling bigots that they're wrong, because their feelings are equally as important. it's obvious that some beliefs experienced as emotion are not worth respecting, and a term like invalidation does not allow one to make that distinction. a refutation can be unfair, demeaning, hypocritical, overly critical, imposing, thoughtless, cruel, etc. i think most of the time the issue is meant to be that the refutation is misplaced—the belief is localized, and shouldn't be judged as a universal. i would add another layer, that the refutation comes from a place of uncontestable authority, often unspoken abstract dictates or truths, rather than a personal, subjective disagreement. as with most psych concepts, this action is defined without reference to power. i think we can do better.

[mist-of-time]

The current in a Resistor-Inductor circuit lags behind voltage

By an angle of pi by two,

that is,

By an angle of ninety degrees.

Ninety degrees! That's the angle between two of the axes on a Cartesian plane,

the angle made by perpendicular lines,

the angle made by the arms of the same clock that tells me it's late, too late.

Does the current ever feel those ninety degrees of late, too late?

Does it alternate between determination and despair where it lags?

But the peculiar thing is that

That same current when flowing in a Resistor-Capacitor circuit leads the voltage

By an angle of pi by two,

that is,

By an angle of ninety degrees.

Another situation altogether, dealing with another electrical component,

And the current leads.

I'm still learning physics

But sometimes it feels like I am current in the RL circuit,

Alternating between determination and despair,

Caught ninety degrees — thirty minutes — too late.

But,

I suppose,

There will come a time,

When I will find myself,

Leading instead,

By ninety degrees,

Still alternating

Between

Determination

And

Despair.

~ phasor diagrams in the twelfth grade [of may the first]

[enetarch-quantum-physics]

Topics to study for Quantum Physics

Calculus

Taylor Series

Sequences of Functions

Transcendental Equations

Differential Equations

Linear Algebra

Separation of Variables

Scalars

Vectors

Matrixes

Operators

Basis

Vector Operators

Inner Products

Identity Matrix

Unitary Matrix

Unitary Operators

Evolution Operator

Transformation

Rotational Matrix

Eigen Values

Coefficients

Linear Combinations

Matrix Elements

Delta Sequences

Vectors

Basics

Derivatives

Cartesian

Polar Coordinates

Cylindrical

Spherical

LaPlacian

Generalized Coordinate Systems

Waves

Components of Equations

Versions of the equation

Amplitudes

Time Dependent

Time Independent

Position Dependent

Complex Waves

Standing Waves

Nodes

AntiNodes

Traveling Waves

Plane Waves

Incident

Transmission

Reflection

Boundary Conditions

Probability

Probability

Probability Densities

Statistical Interpretation

Discrete Variables

Continuous Variables

Normalization

Probability Distribution

Conservation of Probability

Continuum Limit

Classical Mechanics

Position

Momentum

Center of Mass

Reduce Mass

Action Principle

Elastic and Inelastic Collisions

Physical State

Waves vs Particles

Probability Waves

Quantum Physics

Schroedinger Equation

Uncertainty Principle

Complex Conjugates

Continuity Equation

Quantization Rules

Heisenburg's Uncertianty Principle

Schroedinger Equation

TISE

Seperation from Time

Stationary States

Infinite Square Well

Harmonic Oscillator

Free Particle

Kronecker Delta Functions

Delta Function Potentials

Bound States

Finite Square Well

Scattering States

Incident Particles

Reflected Particles

Transmitted Particles

Motion

Quantum States

Group Velocity

Phase Velocity

Probabilities from Inner Products

Born Interpretation

Hilbert Space

Observables

Operators

Hermitian Operators

Determinate States

Degenerate States

Non-Degenerate States

n-Fold Degenerate States

Symetric States

State Function

State of the System

Eigen States

Eigen States of Position

Eigen States of Momentum

Eigen States of Zero Uncertainty

Eigen Energies

Eigen Energy Values

Eigen Energy States

Eigen Functions

Required properties

Eigen Energy States

Quantification

Negative Energy

Eigen Value Equations

Energy Gaps

Band Gaps

Atomic Spectra

Discrete Spectra

Continuous Spectra

Generalized Statistical Interpretation

Atomic Energy States

Sommerfels Model

The correspondence Principle

Wave Packet

Minimum Uncertainty

Energy Time Uncertainty

Bases of Hilbert Space

Fermi Dirac Notation

Changing Bases

Coordinate Systems

Cartesian

Cylindrical

Spherical - radii, azmithal, angle

Angular Equation

Radial Equation

Hydrogen Atom

Radial Wave Equation

Spectrum of Hydrogen

Angular Momentum

Total Angular Momentum

Orbital Angular Momentum

Angular Momentum Cones

Spin

Spin 1/2

Spin Orbital Interaction Energy

Electron in a Magnetic Field

ElectroMagnetic Interactions

Minimal Coupling

Orbital magnetic dipole moments

Two particle systems

Bosons

Fermions

Exchange Forces

Symmetry

Atoms

Helium

Periodic Table

Solids

Free Electron Gas

Band Structure

Transformations

Transformation in Space

Translation Operator

Translational Symmetry

Conservation Laws

Conservation of Probability

Parity

Parity In 1D

Parity In 2D

Parity In 3D

Even Parity

Odd Parity

Parity selection rules

Rotational Symmetry

Rotations about the z-axis

Rotations in 3D

Degeneracy

Selection rules for Scalars

Translations in time

Time Dependent Equations

Time Translation Invariance

Reflection Symmetry

Periodicity

Stern Gerlach experiment

Dynamic Variables

Kets, Bras and Operators

Multiplication

Measurements

Simultaneous measurements

Compatible Observable

Incompatible Observable

Transformation Matrix

Unitary Equivalent Observable

Position and Momentum Measurements

Wave Functions in Position and Momentum Space

Position space wave functions

momentum operator in position basis

Momentum Space wave functions

Wave Packets

Localized Wave Packets

Gaussian Wave Packets

Motion of Wave Packets

Potentials

Zero Potential

Potential Wells

Potentials in 1D

Potentials in 2D

Potentials in 3D

Linear Potential

Rectangular Potentials

Step Potentials

Central Potential

Bound States

UnBound States

Scattering States

Tunneling

Double Well

Square Barrier

Infinite Square Well Potential

Simple Harmonic Oscillator Potential

Binding Potentials

Non Binding Potentials

Forbidden domains

Forbidden regions

Quantum corral

Classically Allowed Regions

Classically Forbidden Regions

Regions

Landau Levels

Quantum Hall Effect

Molecular Binding

Quantum Numbers

Magnetic

Withal

Principle

Transformations

Gauge Transformations

Commutators

Commuting Operators

Non-Commuting Operators

Commutator Relations of Angular Momentum

Pauli Exclusion Principle

Orbitals

Multiplets

Excited States

Ground State

Spherical Bessel equations

Spherical Bessel Functions

Orthonormal

Orthogonal

Orthogonality

Polarized and UnPolarized Beams

Ladder Operators

Raising and Lowering Operators

Spherical harmonics

Isotropic Harmonic Oscillator

Coulomb Potential

Identical particles

Distinguishable particles

Expectation Values

Ehrenfests Theorem

Simple Harmonic Oscillator

Euler Lagrange Equations

Principle of Least Time

Principle of Least Action

Hamilton's Equation

Hamiltonian Equation

Classical Mechanics

Transition States

Selection Rules

Coherent State

Hydrogen Atom

Electron orbital velocity

principal quantum number

Spectroscopic Notation

=====

Common Equations

Energy (E) .. KE + V

Kinetic Energy (KE) .. KE = 1/2 m v^2

Potential Energy (V)

Momentum (p) is mass times velocity

Force equals mass times acceleration (f = m a)

Newtons' Law of Motion

Wave Length (λ) .. λ = h / p

Wave number (k) ..

k = 2 PI / λ

= p / h-bar

Frequency (f) .. f = 1 / period

Period (T) .. T = 1 / frequency

Density (λ) .. mass / volume

Reduced Mass (m) .. m = (m1 m2) / (m1 + m2)

Angular momentum (L)

Waves (w) ..

w = A sin (kx - wt + o)

w = A exp (i (kx - wt) ) + B exp (-i (kx - wt) )

Angular Frequency (w) ..

w = 2 PI f

= E / h-bar

Schroedinger's Equation

-p^2 [d/dx]^2 w (x, t) + V (x) w (x, t) = i h-bar [d/dt] w(x, t)

-p^2 [d/dx]^2 w (x) T (t) + V (x) w (x) T (t) = i h-bar [d/dt] w(x) T (t)

Time Dependent Schroedinger Equation

[ -p^2 [d/dx]^2 w (x) + V (x) w (x) ] / w (x) = i h-bar [d/dt] T (t) / T (t)

E w (x) = -p^2 [d/dx]^2 w (x) + V (x) w (x)

E i h-bar T (t) = [d/dt] T (t)

TISE - Time Independent

H w = E w

H w = -p^2 [d/dx]^2 w (x) + V (x) w (x)

H = -p^2 [d/dx]^2 + V (x)

-p^2 [d/dx]^2 w (x) + V (x) w (x) = E w (x)

Conversions

Energy / wave length ..

E = h f

E [n] = n h f

= (h-bar k[n])^2 / 2m

= (h-bar n PI)^2 / 2m

= sqr (p^2 c^2 + m^2 c^4)

Kinetic Energy (KE)

KE = 1/2 m v^2

= p^2 / 2m

Momentum (p)

p = h / λ

= sqr (2 m K)

= E / c

= h f / c

Angular momentum ..

p = n h / r, n = [1 .. oo] integers

Wave Length ..

λ = h / p

= h r / n (h / 2 PI)

= 2 PI r / n

= h / sqr (2 m K)

Constants

Planks constant (h)

Rydberg's constant (R)

Avogadro's number (Na)

Planks reduced constant (h-bar) .. h-bar = h / 2 PI

Speed of light (c)

electron mass (me)

proton mass (mp)

Boltzmann's constant (K)

Coulomb's constant

Bohr radius

Electron Volts to Jules

Meter Scale

Gravitational Constant is 6.7e-11 m^3 / kg s^2

History of Experiments

Light

Interference

Diffraction

Diffraction Gratings

Black body radiation

Planks formula

Compton Effect

Photo Electric Effect

Heisenberg's Microscope

Rutherford Planetary Model

Bohr Atom

de Broglie Waves

Double slit experiment

Light

Electrons

Casmir Effect

Pair Production

Superposition

Schroedinger's Cat

EPR Paradox

Examples

Tossing a ball into the air

Stability of the Atom

2 Beads on a wire

Plane Pendulum

Wave Like Behavior of Electrons

Constrained movement between two concentric impermeable spheres

Rigid Rod

Rigid Rotator

Spring Oscillator

Balls rolling down Hill

Balls Tossed in Air

Multiple Pullys and Weights

Particle in a Box

Particle in a Circle

Experiments

Particle in a Tube

Particle in a 2D Box

Particle in a 3D Box

Simple Harmonic Oscillator

Scattering Experiments

Diffraction Experiments

Stern Gerlach Experiment

Rayleigh Scattering

Ramsauer Effect

Davisson–Germer experiment

Theorems

Cauchy Schwarz inequality

Fourier Transformation

Inverse Fourier Transformation

Integration by Parts

Terminology

Levi Civita symbol

Laplace Runge Lenz vector

[bubbloquacious]

Extending the D ⊣ U ⊣ I adjunction sequence

Following up on this post, in which I showed that the discrete and indiscrete space functors from the category of sets to the category of topological spaces do not have a left or right adjoint, respectively.

One thing you can notice is that finite products of discrete spaces are discrete. So if we let Finset and Fintop be the categories of finite sets and finite topological spaces (with set functions and continuous maps), then the discrete space functor D: Finset -> Fintop is a continuous functor, unlike the Set -> Top case (note that being 'continuous' as functor requires more than just preserving products, but because I know where this is going I'll just give you that it is in fact continuous). Any time a functor is continuous you should ask yourself whether it has a left adjoint. Let C: Fintop -> Finset be the functor that maps a finite topological space onto its set of connected components. A continuous map induces a set function between the space's connected components, so this does form a functor. For it to be D's left adjoint, we need a natural bijection Finset(CX,A) ↔ Fintop(X,DA) for all finite sets X and finite topological spaces A. This bijection can be constructed if X is any locally connected topological space, because then it is homeomorphic to the disjoint union space of its connected components. Finite topological spaces are Alexandrov-discrete, and Alexandrov-discrete spaces are locally connected, so we have constructed the adjunction.

We have the following functors:

I: Finset -> Fintop, which maps a set onto the indiscrete space on that set, and a set function onto itself which is then automatically continuous.

U: Fintop -> Finset, which maps a topological space onto its underlying set, and a continuous map onto its underlying set function. The forgetful functor.

D: Finset -> Fintop, which maps a set onto the discrete space on that set, and a set function onto itself which is then automatically continuous.

C: Fintop -> Finset, which maps a topological space onto its set of connected components, and a continuous map onto the function it induces between the connected component sets.

We have a sequence of adjunctions C ⊣ D ⊣ U ⊣ I. We know that I is not cocontinuous (the disjoint union space of two indiscrete spaces is usually not the indiscrete space on the disjoint union of their underlying sets), so the sequence stops on the right. Does C have a left adjoint? The set of connected components of a finite product of locally connected topological spaces can naturally be identified with the cartesian product of their sets of connected components. It seems that C preserves products, which does hint towards it being continuous.

We would need a functor F: Finset -> Fintop such that there is a natural bijection Fintop(FA,X) ↔ Finset(A,CX). Consider the case that A is a one point set, and X is a two point space with the indiscrete topology. Then Finset(A,CX) has one element, so Fintop(FA,X) must have one element as well, which forces FA to be the empty space (because there are at least two constant continuous maps, otherwise). If we now take Y = X ⊔ X, then Finset(A,CY) has two elements, but Fintop(FA,Y) still has only one. We conclude that C does not have a left adjoint, so we have a complete sequence of adjoint functors.

[quitepossiblyknot]

"quantum leap exchanged for a decent heading" - by Ekow Arthur $prismelanin *

Singularity, in carrying a single image, distal, gripping

Finger dithers, it soon is vestige, fits to what's augmented

An authentic position in getting the picture, switch first

Reaching the village, lungs filling, swelling of this worth

Sovereign, no longer impoverished, the coverage of what governs mental isn't obscured, what knowledge is stronger, pouring into her fixed cure

Ensure the lineage, to see a future with ya girl, leverage, which swirls a galaxy

Beginning of friends naturally, connection is a tapestry

Fist twirls to remove monitoring spirits, clearing the air, the feeling is weird of conquering appearances

Mask off, facing demons, slaying even ghosts, the impossible was finished

Shifting paradigm, pair of eyes remote view, paraphrase, phase loop, to go through a portal sorta scared

Time dilated, immortal here, all praise to free quince

Distorted lair, transported pair to a marble square where every fractal is a warp to stare in hyperspace

Hyper plane, parallel, imposition for the Cartesian points, important shares, no one cares about Elysian voiced, for the field is solely ours

So we scour to know da hours are nanoseconds, canon to apprehension, can't go to where average tech is

Fixture to flesh is atoms, Madame, over here we electron scattering, select how matter is, weapons shattered beyond fragmented, incandescent to select now

Gathering, reported fear so I recorded chairs in vestigial, preliminary, interosseous ligament to visual, isn't scary anymore

Marbling for every floor, figured out what you took my hand for, as tours of the universe in hyperdimension extended to this moment

Had to extrapolate at rates to gather the components

High off ya love, this is what a dose is

Every extract of channeling is a dosage

Deep conversations was the doses

Most is asleep to frequencies, however we entered where the frequenting of these speeds quantify as decent leaps

Quanta in the fourth

Marbles for a knob, remember all the keys I gave you, now we're at the door

Don't marvel at the stars, our ancestors stuck together for this momentous occasion, we made it here after all

Didn't make sense how you mentioned friends, it didn't connect then, koan to Zen when presented a message in text, lexicon of a kiss

Baby, you upper echelon with a twist

How do explain a rabbit hole and a trip?

The signet ring with its symbol evolved our subconscious to dissolve and what appeared before us was Cygnus Wall

Akashic records whispers tall, wherewithal of a knuckle to get this far

How'd we get here? At the knick of time when we hit 8 ball, enriched which corridor, to sink, installed, what you're afraid of is bliss with pause

It hits different when it's within walls, Richter, scale

If you cared as much as I do, next flight moves, dare light groove faster than our frequency

Frequenting your virgin Mary, symbolism of 8,000 nerves, masonry isn't scary in instances as profound as her depths, bending space to curve what's left of gravity

We slowed it down enough to access what would rapidly get us right, universe to verses, candidly in sight a momentum to where the hand is south of horizon like

Pisces on the cusp of Aries, prime meridian of eye, sine to tangent, wavicle for quantum slide, time of my life

Counted each variant to account for a tear in the sky, maybe anti-vertex was an exaggeration of why the two of us are inseparable to a vibe

Twin flames at the decan of Aquarius, the carriers of dragonflies to compare the signs is ecliptic to this disc inside what's squared to this square of mine

Circling four corners, boundaries made for borders, incantations as brick & mortar, stabilizing finally from dilation that distorted

Transposition of Rick & Morty, rook is little miss bun cake and Capricorn is king, my 10th house at the brink, vertex to the west for sagittal in plane, clear ya sinus just to think, Sagittarius in stellium, tropical to blink

Alchemizing helium, neon in the pink

Castor oil topical, told you to make room for the illogical

Eons in the brink, heaven too shall pass so I had gamma rays to waves, distinct to a particle

Magic in a computation, forwarded an article

Arxvis

Jargon might not be completely understood, knock on wood

Phase lock to the west, what's next to Scorpio is mood to the oud, so what's good?

Bear with me while Virgo is sigmoid to the hood, colon, ratio of unit for a move, we're growing in guiding

Souls realizing they're healthy for each other is a helping of another in the other world

Otherworldly motherboard, matrices to cover pearls

Never cast to swine

Axis vertebra, reverse the weight, reverberates to match divine

At the center of a nebula, don't you dare ask me the time

Unexpected brat fell in my lap, so now I share the shine, justified emanation, explanation for the beacon, steradian was seeking me in a sequence of preparing this to prime vertical, working both Leo and Cancer

Neo in answer, timeless is where passion and joy find themselves carried away

Yod of orb, five on the face of die, northeast to a trace of nigh

Gemini, my dear

Nadir

I fear we got too close

Closing this portal for the portico, the sorta soul to program hematite

Even I make mistakes, seems polite to forewarn

Energetic signature to your warm is more for what's universal

Taurus at the midheaven, northeast to our core

Hopefully you've caught on... How many months til u get it? Need four more? 👀

Toroid in her for sure

Two things for certain, working to unite entails that inner workings serve a purpose and the circling of purple is what works in stating service

Coloring uncovering auric field to serving what's magnetic in electric flux, who knew prime meridian was circuits to computation of selected touch to let in lovingly what a seed speaks to breed kinks

Ovulation

Contemplating higher realms, she's drawn to how I'm constellation, now we delve to discovering what it takes

Angstrom to oersted, undulate

Interatomic distances, forehead kisses, misses is instinctive with conscious decisions, skipping stones to asteroid belts, extract voids well enough to living poem, neutrino entelechy, spreading both her cheeks between a smile and the webbing

Sticky situation thinking of a title for the heading

Blogging something nuanced to seeing where she is headed

Felatio is head if sentence is in an ending, period near Sirius is Ceres at the wedding

Intentions as pure is this is seeing where I'm heading

Feeding curiosity to recently a sending of right ascension while ascending

I don't know how to express a micro-dose, my ascendent sign is your rise, what arises in a quest is how the best is face-to-face and why I'm tending to a poetic styling, the emphasis is finding out directly

Even if I'm teacher it doesn't mean I don't stand correcting, to plans erecting

Planets projecting what a section of an upgrade is, what phase is lunar to the sooner that we get it

** her favorite underdog

* for now, I only have love to give...

Quitepossiblyknot ©

The Cygnus Wall

[govindhtech]

New Python Package And Quantum Machine Learning Models

Combining machine learning and quantum computing,  quantum machine learning (QML) is an interdisciplinary field that is rapidly expanding. Studying how machine learning can be applied to quantum problems and how quantum systems might enhance machine learning is fascinating. Python is vital in this business because to its robust libraries and frameworks.

Introduction to Quantum Machine Learning and Python

Machine learning or quantum computing expert to learn QML. Quantum computing, which began in physics research, is now available to high school students as software. Math and linear algebra are the key requirements, along with basic Python. Trigonometry, vectors, matrices, polar and Cartesian coordinate systems, complex numbers, functions, gradients, eigenvalues, eigenvectors, and linear combinations are important math concepts. Although a basic understanding is sufficient, understanding qubit representation and manipulation requires these mathematical building blocks.

Python underpins numerous prominent classical and quantum machine learning tools and frameworks, including PyTorch, scikit-learn, and PennyLane. Free online courses or, if you've coded before, grammar videos, cheat sheets, and little projects are good ways to learn Python. QML benefits from NumPy, a popular Python scientific computing library.

After mastering these basics, you can study QML's three pillars: optimisation, machine learning, and quantum computing.

Optimisation is crucial and often involves minimising a “cost function” through progressive “cost landscape” modifications. Optimisation methods use gradient, which shows a function's steepest change, to find the lowest cost point.

Machine learning allows computers to recognise patterns in data and extrapolate them to new data without programming. This may involve training a model on a dataset, optimising a cost function, then testing it on a new dataset to ensure broad trends. The correct prediction rate or squared distance between model output and label, which is useful for gradient-based optimisation due to its continuity, can be used to measure classification progress.

Quantum computing QML tasks often use neural networks, a key machine learning concept. They are trained using backpropagation to estimate the gradient of the cost function with respect to the weights and have nodes and weighted edges that process data from inputs to outputs. Besides picture classification, machine learning tasks include regression, clustering, and reinforcement learning.

Physical quantum systems and their special characteristics are used in quantum computing to perform calculations. Quantum computers employ qubits, such as photons, superconducting qubits, or trapped ions, in contrast to classical computers. Qubits, which are complex-valued unit vectors or their linear combinations, are the building blocks of quantum information.

The idea of superposition, in which a qubit might be 0 or 1 like a spinning coin, is crucial. Entanglement and interference are also used in computation. Qubit gates, which are similar to classical logic gates, can superpose, entangle, and change measurement probabilities. These processes are usually depicted as a quantum circuit with gates and qubit wires. The final measurement compresses superpositions into classical states.

Quantum machine learning Python packages: PennyLane and Beyond

Combining these components makes Python packages crucial. PennyLane, a cross-platform Python quantum computer programming package with differentiability, is an example. This makes writing and running quantum computing algorithms easier and allows customers to use quantum computers from multiple manufacturers.

The following steps are typical for PennyLane QML program development:

Explain a device: State its quantum device type (e.g., ‘default.qubit’ simulator) and how many qubits (wires) it needs.

Define your quantum circuit (QNode): Write a Python function that performs the quantum circuit and returns a measurement using parameters.

Describe optional pre-/postprocessing: Hybrid models often use preprocessing or postprocessing methods like simple additions or complex neural networks.

Define cost function: Your QNode output and any traditional pre/postprocessing are used to minimise this Python function during training.

Execute optimisation: Choose an optimiser (PennyLane offers many).

Determine step size.

Quantum circuit parameters should be estimated beforehand. Repeat a set number of times to lower costs and adjust parameters.

Appreciate your results: Print or graph the optimisation result to see if the model found the data pattern.

Training a quantum circuit to replicate a sine function shows how to train a quantum model to recognise patterns.Outside PennyLane, specialised Python packages are being created. A new Python library that extends PennyLane's capabilities was designed to simplify Fourier model analysis and training for quantum machine learning models. This program, detailed in “QML Essentials A framework for working with Quantum Fourier Models” by Melvin Strobl, Maja Franz, Eileen Kuehn, Wolfgang Mauerer, and Achim Streit, provides strong analytical tools to understand QML model behaviour and maximise performance.

The main features

Main characteristics of this new package:

Noise addition: By merging different noise models, it can replicate genuine quantum hardware conditions, helping researchers test algorithm resilience and create noise-resistant circuits.

Circuit parameter initialisation methods: The package offers several approaches that can affect training and model quality.

Expression and entanglement calculations: These assess a model's learning and generalisation to new inputs. Expressibility is a circuit's ability to match any target function, while entanglement measures quantum interactions.

Fourier spectrum calculations: It uses two methods to calculate a quantum circuit's Fourier spectrum: an analytical trigonometric polynomial expansion method and the computationally efficient Fast Fourier Transform. This reveals the circuit's core dynamics and capabilities, revealing optimisation options.

Because the package is modular, the quantum machine learning community may simply add new features and encourage code reuse and collaboration. The development team values community feedback and strives towards improvement.

A new Python library, LazyQML, benchmarks and compares many QML models based on architectures and ansatzes from the literature. The conference paper LazyQML addresses the lack of a clear and systematic framework for comparing QML models due to the rapid expansion of quantum computing and the rapidly evolving QML frameworks like Qiskit and PennyLane.

In conclusion, Python libraries like PennyLane make QML accessible by defining quantum circuits, integrating them into machine learning algorithms, and optimising. Dedicated benchmarking packages like LazyQML and PennyLane's Fourier model extension improve the capacity to analyse, train, and compare complex QML models.

[deltastark]

Industrial Robots: Powering the Future of Smart Manufacturing

In today’s rapidly evolving industrial landscape, industrial robots are more than just machines — they’re the driving force behind productivity, precision, and innovation. From automotive to electronics, packaging to pharmaceuticals, industrial robots are transforming the way goods are produced, handled, and delivered.

Whether it’s assembling components, moving materials, or performing repetitive tasks with flawless consistency, industrial robots are at the core of modern automation. In this article, we’ll explore what industrial robots are, how they work, their types, benefits, and why more companies are investing in robotic automation than ever before.

What Are Industrial Robots?

Industrial robots are programmable, automated machines used to perform specific tasks in manufacturing or industrial environments. These tasks can include welding, painting, assembly, material handling, packaging, palletising, inspection, and testing.

Industrial robots are designed to replace or assist human workers in tasks that are dangerous, repetitive, or require extreme precision. They can be fixed or mobile, and often operate within a robotic cell or assembly line.

Types of Industrial Robots

Articulated Robots These have rotary joints and resemble a human arm. They are highly flexible and used for welding, assembly, and material handling.

SCARA Robots (Selective Compliance Articulated Robot Arm) Ideal for high-speed pick-and-place tasks, assembly, and packaging.

Cartesian Robots These operate on three linear axes (X, Y, and Z) and are great for CNC machines, 3D printing, and heavy load handling.

Delta Robots Known for speed and precision, they’re commonly used in packaging and pharmaceutical applications.

Collaborative Robots (Cobots) Designed to safely work alongside humans, cobots are ideal for small and medium enterprises seeking flexible automation.

Applications of Industrial Robots

Automotive: Welding, assembling chassis, and painting.

Electronics: Precise placement of micro-components.

Packaging: High-speed product picking, labeling, and boxing.

Pharmaceuticals: Sterile product handling and packaging.

Food & Beverage: Sorting, filling, and palletizing operations.

Benefits of Using Industrial Robots

Increased Productivity Robots can work 24/7 with consistent speed and accuracy, significantly increasing output.

Improved Product Quality Precision programming ensures that every task is performed identically, reducing defects and waste.

Reduced Labor Costs Robots minimize the need for manual labor in repetitive or hazardous jobs, saving costs over time.

Workplace Safety By taking over dangerous tasks, robots reduce the risk of injury to workers.

Faster Time-to-Market Automation accelerates the production cycle, helping companies meet market demands quicker.

Scalability and Flexibility Robotic systems can be reprogrammed or scaled to suit new products or production changes.

The Future of Industrial Robotics

The industrial robotics market in India and worldwide is growing at a remarkable pace, thanks to advances in AI, machine vision, IoT, and predictive maintenance. Robots are no longer confined to repetitive tasks — they are learning, adapting, and collaborating.

With the rise of smart factories and Industry 4.0, companies are leveraging robotics to optimise supply chains, reduce errors, and gain real-time data insights. As the demand for efficiency and customisation increases, so will the adoption of industrial robots across sectors.

Delta Stark Engineering: Your Partner in Industrial Automation

At Delta Stark Engineering, we specialize in designing and delivering high-performance industrial robots that meet your unique manufacturing needs. From pick and place systems to packaging automation, our robots are built for speed, precision, and long-term reliability.

We offer:

Customized automation solutions

Integration with existing systems

Full support and service across India

Whether you're upgrading your production line or building a smart factory from scratch, our robotic systems empower your business to operate smarter, safer, and faster.

[datastring]

Cartesian Pick And Place Machine Market Forecast to Reach $338.1 Million by 2035

The Cartesian Pick And Place Machine market is expected to grow significantly, with industry revenue projected to increase from $197.7 million in 2024 to $338.1 million by 2035. This growth corresponds to an average annual rate of 5.0% over the forecast period.

Detailed Analysis - https://datastringconsulting.com/industry-analysis/cartesian-pick-and-place-machine-market-research-report

Key Applications Driving Market Demand

Cartesian Pick And Place Machines are crucial across various applications including:

Packaging and palletizing

Assembly operations

Testing and inspection

Material handling

These applications underscore the machine’s vital role in automation across multiple industries.

Market Segmentation and Growth Opportunities

The market analysis covers technology types, applications, product categories, operating speeds, and industries served. These factors reveal significant opportunities for revenue expansion and technological innovation.

Industry Leadership and Competitive Landscape

The Cartesian Pick And Place Machine market is highly competitive, with major players such as:

Yamaha Corporation

Bosch Rexroth AG

Schneider Electric

Festo

ABB Ltd

Mitsubishi Electric Corporation

DENSO Corporation

Stubli International AG

Panasonic Corporation

Hirata Corporation

Seiko Epson Corporation

Rockwell Automation Inc.

These companies drive the market forward through continuous innovation and adoption of advanced automation technologies.

Growth Drivers: Packaging Demand and Technological Advancements

Rising demand in packaging industries and ongoing advancements in automation technology are key factors propelling market growth. The surge in the electronic assembly sector further supports the increasing adoption of Cartesian Pick And Place Machines.

Regional Trends and Supply Chain Evolution

North America and Europe remain the leading regions for Cartesian Pick And Place Machines. Despite challenges like high initial investments and rapid technological changes, the supply chain—from raw materials procurement, component manufacturing, assembly, and testing to distribution and sales—is evolving.

To diversify revenue and expand the total addressable market (TAM), industry players are also targeting emerging markets such as Indonesia, Nigeria, and Chile for strategic growth.

About DataString Consulting

DataString Consulting provides comprehensive market research and business intelligence services for both B2C and B2B sectors. With over 30 years of combined experience, their leadership team delivers customized market research projects aligned with clients’ strategic goals.

The company specializes in strategy consulting, opportunity assessment across diverse industries, and solution-driven approaches to business challenges. DataString Consulting’s industry experts monitor high-growth sectors across more than 15 industries, offering timely and actionable insights worldwide.

[norimtarna]

The current in a Resistor-Inductor circuit lags behind voltage

By an angle of pi by two,

that is,

By an angle of ninety degrees.

Ninety degrees! That's the angle between two of the axes on a Cartesian plane,

the angle made by perpendicular lines,

the angle made by the arms of the same clock that tells me it's late, too late.

Does the current ever feel those ninety degrees of late, too late?

Does it alternate between determination and despair where it lags?

But the peculiar thing is that

That same current when flowing in a Resistor-Capacitor circuit leads the voltage

By an angle of pi by two,

that is,

By an angle of ninety degrees.

Another situation altogether, dealing with another electrical component,

And the current leads.

I'm still learning physics

But sometimes it feels like I am current in the RL circuit,

Alternating between determination and despair,

Caught ninety degrees — thirty minutes — too late.

But,

I suppose,

There will come a time,

When I will find myself,

Leading instead,

By ninety degrees,

Still alternating

Between

Determination

And

Despair.

~ phasor diagrams in the twelfth grade

[dropshipautomation]

Advancing Automation: Innovating Industries with Key Technologies

In today's dynamic industrial landscape, automation stands as a cornerstone of efficiency, safety, and sustainable progress. At Dropship Automation Solutions, we specialize in providing premium automation components essential for optimizing operations across diverse industries. In this article, we explore three pivotal components crucial for any automation setup: actuators, industrial robots, and SCADA systems. Whether you're upgrading existing systems or embarking on new installations, understanding these components is essential for achieving peak operational performance.

1. Actuators: Precision in Motion

What are Actuators in Automation? Actuators are mechanical or electromechanical devices that convert energy into motion, driving essential industrial processes with precision and reliability.

Key Types and Applications:

Types: Pneumatic actuators, hydraulic actuators, electric actuators

Applications: Valve control, robotics, material handling

Benefits: High precision, rapid response times, robust performance

Why Actuators Matter: Actuators play a crucial role in automation by enabling precise control over mechanical movements, ensuring optimal efficiency and productivity in industrial operations.

2. Industrial Robots: Transforming Manufacturing

What are Industrial Robots in Automation? Industrial robots are programmable machines designed to perform tasks traditionally handled by human workers, enhancing production capabilities and efficiency.

Key Features and Importance:

Types: Articulated robots, Cartesian robots, collaborative robots (cobots)

Functions: Assembly, welding, painting, palletizing

Applications: Automotive assembly lines, electronics manufacturing, logistics

Why Industrial Robots Matter: Industrial robots streamline manufacturing processes, improving accuracy, reducing cycle times, and enhancing workplace safety by automating repetitive or hazardous tasks.

3. SCADA Systems: Enhancing Control and Monitoring

What are SCADA Systems in Automation? SCADA (Supervisory Control and Data Acquisition) systems are software and hardware solutions used for real-time monitoring and control of industrial processes.

Key Components and Applications:

Components: Remote terminal units (RTUs), human-machine interface (HMI), communication infrastructure

Functions: Data acquisition, process visualization, alarm management

Applications: Power plants, water treatment facilities, oil and gas refineries

Why SCADA Systems Matter: SCADA systems facilitate centralized monitoring and control of complex industrial operations, optimizing efficiency, minimizing downtime, and ensuring regulatory compliance.

Integration for Seamless Automation

Imagine a scenario where:

Actuators ensure precise positioning and control in automated assembly lines.

Industrial robots collaborate seamlessly in manufacturing processes, enhancing production throughput.

SCADA systems monitor critical parameters in real-time, enabling proactive maintenance and operational adjustments.

Conclusion

Automation continues to redefine industrial processes by boosting productivity, ensuring operational reliability, and fostering sustainable growth. By integrating essential components like actuators, industrial robots, and SCADA systems, industries can achieve unparalleled efficiency, lower operational costs, and gain a competitive edge in today's global marketplace.

At Dropship Automation Solutions, we are committed to delivering cutting-edge automation solutions tailored to your specific needs. Explore our comprehensive range of automation components or contact us for personalized consultation and support on your automation journey.

Contact: +1 (234) 288-1755 Email: sales@dropshipautomation.com Location: 1440 W. Taylor St #2555, Chicago, IL 60607

[my-traumerei]

Understanding the Grammar of Graphics in R

The Grammar of Graphics is a conceptual framework for data visualization that allows you to create a wide range of plots using a consistent set of principles. It forms the foundation of the ggplot2 package in R, enabling you to build complex and layered visualizations in a systematic way. Understanding this grammar will not only help you use ggplot2 effectively but also give you deeper insights into how data visualization works at a fundamental level.

1. The Concept of the Grammar of Graphics

The Grammar of Graphics, introduced by Leland Wilkinson in his 1999 book, is a theoretical approach to visualization that breaks down the process of creating a plot into a set of independent components. Each plot is constructed by layering these components, much like how a sentence in language is constructed using grammar.

Key Components:

Data: The dataset that contains the information you want to visualize.

Aesthetics (aes): The visual properties of the plot, such as position, color, size, and shape, which are mapped to variables in your data.

Geometries (geom): The type of visual element used to represent the data, such as points, lines, bars, or boxplots.

Scales: The mappings from data values to visual properties, such as how data values are translated into axis positions, colors, or sizes.

Facets: The division of data into subplots based on a categorical variable, allowing for the comparison of subsets of data.

Coordinates: The system that determines how data points are mapped onto the plot, such as Cartesian coordinates or polar coordinates.

Layers: The different components or elements added on top of each other to build the final plot.

2. Building a Plot Using the Grammar of Graphics

In ggplot2, each plot is constructed using layers, where each layer represents one or more of the components of the Grammar of Graphics. The process typically starts with defining the data and aesthetics, followed by adding geometries and other components.

Basic Plot Structure:

ggplot(data = dataset, aes(x = x_variable, y = y_variable)) + geom_point()

Data: The data argument specifies the dataset you want to use.

Aesthetics: The aes() function maps variables from the dataset to visual properties like the x and y axes.

Geometry: geom_point() adds a layer of points to the plot, creating a scatter plot.

3. Understanding Aesthetics (aes)

Aesthetics in ggplot2 refer to how data variables are mapped to visual properties. These mappings determine how your data is visually represented in the plot.

Common Aesthetics:

x and y: The variables mapped to the x and y axes.

color: The color of points, lines, or bars, which can be mapped to a categorical or continuous variable.

size: The size of points or lines, often mapped to a continuous variable.

shape: The shape of points in a scatter plot, typically used with categorical variables. Example:

ggplot(data = dataset, aes(x = x_variable, y = y_variable, color = category_variable)) + geom_point()

4. Working with Geometries (geom)

Geometries in ggplot2 define the type of plot you create, such as a scatter plot, line plot, bar chart, or histogram. Each geometry function corresponds to a different type of plot.

Common Geometries:

geom_point(): Creates a scatter plot.

geom_line(): Creates a line plot.

geom_bar(): Creates a bar chart.

geom_histogram(): Creates a histogram.

geom_boxplot(): Creates a boxplot.

Example:ggplot(data = dataset, aes(x = x_variable, y = y_variable)) + geom_line()

5. Understanding Scales and Coordinates

Scales in ggplot2 control how data values are mapped to visual properties, such as the position on the axes, colors, or sizes. Coordinates define the plotting area and how data points are placed within it.

Scales:

scale_x_continuous() and scale_y_continuous(): Adjust the continuous scales of the x and y axes.

scale_color_manual(): Customize color scales.

scale_size_continuous(): Customize the size scale.

Example:ggplot(data = dataset, aes(x = x_variable, y = y_variable, color = category_variable)) + geom_point() + scale_color_manual(values = c("red", "blue"))

Coordinates:

coord_cartesian(): Adjust the limits of the plot without affecting the data.

coord_flip(): Swap the x and y axes.

coord_polar(): Convert Cartesian coordinates to polar coordinates for circular plots.

Example:ggplot(data = dataset, aes(x = factor_variable, y = value_variable)) + geom_bar(stat = "identity") + coord_flip()

6. Faceting for Comparison

Faceting allows you to create multiple subplots based on the values of a categorical variable, enabling you to compare different subsets of data.

Faceting Functions:

facet_wrap(): Creates a series of plots wrapped into a grid.

facet_grid(): Creates a grid of plots based on the combination of two categorical variables.

Example:ggplot(data = dataset, aes(x = x_variable, y = y_variable)) + geom_point() + facet_wrap(~ category_variable)

7. Combining Layers to Build Complex Plots

One of the powerful aspects of the Grammar of Graphics is the ability to layer multiple geometries and aesthetics in a single plot. This allows you to create complex visualizations that convey more information.

Example of a Multi-Layer Plot:

ggplot(data = dataset, aes(x = x_variable, y = y_variable)) + geom_point() + geom_smooth(method = "lm", se = FALSE) + labs(title = "Scatter Plot with Linear Regression Line")

In this example, geom_point() adds the points to the plot, while geom_smooth() overlays a linear regression line.

The Grammar of Graphics provides a powerful framework for understanding and creating data visualizations in R using ggplot2. By breaking down the components of a plot into layers, aesthetics, geometries, scales, coordinates, and facets, you can systematically build complex and meaningful visual representations of your data. Mastering this grammar is essential for creating effective visualizations that can reveal insights and support data-driven decision-making.

Full coverage at Strategic leap

[semiconductorsandelectronics]

3D Printing Robot Market Size, Share & Industry Trends Analysis Report by Component (Robot Arms, 3D Printing Heads, Software), Robot Type (Articulated Robots, Cartesian Robots, SCARA Robots, Polar Robots, Delta Robots), Application, End-user Industry and Region - Global Forecast to 2028

[chaitanya]

What is a Cartesian robot, and how is it utilized in automation?

A cartesian robot is also known as a Gantry robot. It is a type of robotic system which moves in straight lines along the orthogonal axes. It is commonly referred to as the X, Y and Z axes. These robots are bolts on a coordinate system. They follow Cartesian geometry, and therefore, they have their name.

It involves movements in right-angled directions. Each axis of movement is powered by either a motorized system or a linear actuator. It enables the robot to move accurately in a predictable and controlled manner.

Critical characteristics of Cartesian robots

The following are the essential characteristics of cartesian robots.

Structure

Caterina robots consist of three linear actuators positioned perpendicular to each other. This enables the robot to move in three-dimensional space. Some designs might include an additional rotational axis, referred to as the "R-axis." It helps enhance the robots' capability.

Design simplicity

The construction is straightforward; therefore, cartesian robots are relatively simple to function, design, and maintain compared to the other types of Industrial robotics. Such simplicity also translates to excellent eater reliability and lower costs.

Scalability

The linear axes of a cartesian robust can be scaled and customized to meet particular operational needs. The length of each axis can be shortened or extended on the basis of the size of the work area, making it significantly adaptable to different applications.

High precision

Cartesian robots are known for their precision and accuracy. It makes them ideal for tasks that require meticulous positioning and movement. The linear motion control of the linear robot helps it follow predefined paths with minimal errors, contributing to high repeatability. Cartesian robots are widely employed in industrial automation due to their affordability, cost-effectiveness, and ease of integration.

Their linear action is perfect for many different kinds of jobs, especially those that need basic, repeated movements. The following are some of the leading automation applications for Cartesian robots:

Material Management

Every Cartesian robot is extensively utilized in material handling applications. They can handle delicate parts with greater accuracy and reproducibility, lowering the possibility of damaging the materials. They are employed in sectors where precision and consistency are essential.

3D printing

3D printing is one of the most renowned uses for Cartesian robots. This makes it possible to precisely deposit material in layers to form intricate patterns and motifs. Cartesian robots are perfect for usage in tiny desktop 3D printers and extensive industrial additive manufacturing equipment because of their precision and scalability. The printed products' structural integrity and dimensional precision are guaranteed by their exact movement along the three axes.

Final words

Cartesian robots are a vital component of the automation landscape. Their adaptability across various sectors is demonstrated by their application in palletizing, automated inspection, 3D printing, material handling, and CNC machining.

As automation technology advances, Cartesian robots are expected to significantly enhance operational precision and efficiency in manufacturing and other industries. Reach out to Igus for the best products and services. We ensure you the most affordable yet proficient and effective products. So, contact us and communicate your requirements without any delay!

[globalgrowthinsights]

Ceramic Packages Market 2024: Emerging Trends, Major Driving Factors, Business Growth Opportunities

Ceramic Packages Market provides in-depth analysis of the market state of Ceramic Packages manufacturers, including best facts and figures, overview, definition, SWOT analysis, expert opinions, and the most current global developments. The research also calculates market size, price, revenue, cost structure, gross margin, sales, and market share, as well as forecasts and growth rates. The report assists in determining the revenue earned by the selling of this report and technology across different application areas.

Geographically, this report is segmented into several key regions, with sales, revenue, market share and growth Rate of Ceramic Packages in these regions till the forecast period

North America

Middle East and Africa

Asia-Pacific

South America

Europe

Key Attentions of Ceramic Packages Market Report:

The report offers a comprehensive and broad perspective on the global Ceramic Packages Market.

The market statistics represented in different Ceramic Packages segments offers complete industry picture.

Market growth drivers, challenges affecting the development of Ceramic Packages are analyzed in detail.

The report will help in the analysis of major competitive market scenario, market dynamics of Ceramic Packages.

Major stakeholders, key companies Ceramic Packages, investment feasibility and new market entrants study is offered.

Development scope of Ceramic Packages in each market segment is covered in this report. The macro and micro-economic factors affecting the Ceramic Packages Market

Advancement is elaborated in this report. The upstream and downstream components of Ceramic Packages and a comprehensive value chain are explained.

Browse More Details On This Report at @https://www.globalgrowthinsights.com/market-reports/ceramic-packages-market-100566

 Global Growth Insights

Web: https://www.globalgrowthinsights.com

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