Location Of Zeros Research Articles

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

In this article, wave based method (WBM) is proposed as a new semi-analytical method to analyze the wave propagation characteristics of the magneto-electro-thermo-elastic nanobeams with arbitrary boundary conditions. According to the Timoshenko beam theory and Hamilton principle, the governing equations of the nanobeam which are related to Eringen’s nonlocal theory are obtained. The displacement and external potential variables are expanded as wave function forms. In the light of the introduction of several type boundary conditions, the total matrix of the nanobeam is constituted. Searching the zero locations of the total matrix determinant by the bisection method, the natural frequencies of the nanobeam under arbitrary boundary conditions are received. To further illustrate the calculation correctness of the presented method, the results are compared with the solutions in reported references. Furthermore, a series of numerical examples are proposed to investigate the effect of each parameter on the free vibration characteristics of the nanobeam with several boundary conditions, such as beam length and thickness, external temperature rise, magnetic and electric potential. Some new numerical solutions and conclusions are presented in this paper to provide the basic foundation for subsequent research.

TECHNIQUE OF THE TESTING OF PSEUDORANDOM SEQUENCES

The article is dedicated to systematization of scientific positions about the static testing of sequences, widely used in cryptographic systems of information protection for the production of key and additional information (random numbers, vectors of initialization, etc.). Existing approaches to testing pseudorandom sequences, their advantages and disadvantages are considered. It is revealed that for sequences of length up to 100 bits there are not enough existing statistical packets. Perspective direction of research – static testing of sequences using n- dimensional statistics is considered. The joint distributions of 2-chains and 3-chains of a fixed type of random (0, 1) -sequences allow for statistical analysis of local sections of this sequence. Examples, tables, diagrams that can be used to test for randomness of the location of zeros and ones in the bit section are 16 lengths. The paper proposes a methodology for testing pseudorandom sequences, an explicit form of the joint distribution of 2- and 3-chains numbers of various options of random bit sequence of a given small length is obtained. As a result of the implementation of this technique, an information system will be created that will allow analyzing the pseudorandom sequence of a small length and choosing a quality pseudorandom sequence for use in a particular subject area.

Sharp Bounds for Asymptotic Characteristics of Growth of Entire Functions with Zeros on Given Sets

This paper provides an overview of the latest research on the two-sided estimates of classical characteristics of growth of entire functions such as the type and the lower type in terms of the ordinary or average densities of the distribution of zeros. We give also accurate estimates of the type of an entire function, taking into account additionally the step and the lacunarity index of the sequence of zeros. The results under consideration are based on the solution of extremal problems in classes of entire functions with restrictions on the behavior of the zero set. Particular attention is paid to the following important cases of the location of zeros: on a ray, on a straight line, on a number of rays, in the angle, or arbitrarily in the complex plane.

SURVEY AND ADJUSTMENT OF CONTROLLER OF A GRAPH-ANALYTICAL METHOD TO A SECOND ORDER OBJECT

This paper proposes to adjust the controller using a graph-analytical method in the complex plane. The various configurations regarding the location of zeros and poles to those of the object are also considered. Adjusted controllers are surveyed, such as they are integrated into control systems, and some of the quality indicators of an automatic control system are analyzed.

Riemann Hypothesis from the Physicist’s Point of View

This article presents an attempt to comprehend the evolution of the ideas underlying the physical approach to the proof of one of the problems of the century - the Riemann hypothesis regarding the location of non-trivial zeros of the Riemann zeta function. Various formulations of this hypothesis are presented, which make it possible to clarify its connection with the distribution of primes in the set of natural numbers. A brief overview of the main directions of this approach is given. The probable cause of their failures is indicated - the solution of the problem within the framework of the classical Turing paradigm. A successful proof of the Riemann hypothesis based on the use of a relativistic computation model that allows one to overcome the Turing barrier is presented. This model has been previously applied to solve another problem not computable on the classical Turing machine - the calculation of the sums of divergent series for the Riemann zeta function of the real argument. The possibility of using relativistic computing for the development of artificial intelligence systems is noted.

Filter Order and Transmission Zeroes Calculation of Crosscoupled Resonator filters

Determination of filter order and transmission zeroes is the precondition of synthesizing cross-coupled filters. Firstly, we propose a method to determine them according to given filter specifications using Genetic Algorithm. The effective objective function is proposed for Genetic Algorithm. We can obtain the least filter order and the optimum locations of transmission zeros to fulfil filter specifications by this method.

Quasi-orthogonality and zeros of some [formula omitted] and [formula omitted] polynomials

We state and prove the q-extension of a result due to Johnston and Jordaan (cf. Johnston and Jordaan (2015)) and make use of this result, the orthogonality of q-Laguerre, little q-Jacobi, q-Meixner and Al-Salam–Carlitz I polynomials as well as contiguous relations satisfied by the polynomials, to establish the quasi-orthogonality of certain 2ϕ2 and 3ϕ2 polynomials. The location and interlacing properties of the real zeros of these quasi-orthogonal polynomials are studied. Interlacing properties of the zeros of q-Laguerre quasi-orthogonal polynomials Ln(δ)(z;q) when −2<δ<−1 with those of Ln−1(δ+1)(z;q) and Ln(δ+1)(z;q) are also considered.

The impact of fluctuations on the zeros of the energy probability distribution

In this communication we explore the possible effects of statistical fluctuations on the use of the Energy Probability Distribution (EPD) zeros to study phase transitions. In the EPD zeros technique one has to find the roots of a polynomial whose coefficients are given by the EPD - a histogram of energy values obtained in a Monte Carlo simulation, for example. Phase transitions are signalized by the presence of a zero that approaches the point (1,0) in the complex plane. Once the EPD estimations are usually subject to statistical fluctuations and polynomial roots are known to be sensitive to modifications in its coefficients, we have compared the roots of a given polynomial with the roots of a perturbed one, searching for possible impacts on the method. Our results show that although the overall map of zeros is modified, the location of the dominant zero, the one that indicates the presence of a phase transition, is not affected. Indeed, even for 30% perturbation only small modifications in the dominant zero location is observed.

Bandpass filter based on asymmetric funnel shaped resonators with ultra wide upper stopband characteristics

A novel microstrip bandpass filter with wide passband, good skirt selectivity and very good passband reflection characteristics using asymmetric funnel shaped resonators is presented in this paper. IE3D simulation software is used for the design and analysis of the proposed filter and the electric field intensities at various frequencies of interest are plotted and verified the role of even and odd mode resonances in achieving wide passband. There are six modes, including three even and three odd modes for the developed filter. Novel equations are derived for finding out the location of transmission zeros and the role of resonators in achieving sharp selectivity are verified. The out of band performance of filter is very good with a suppression level greater than 20 dB upto 24.2 GHz. The centre frequency of the filter is 5.68 GHz with a fractional bandwidth of 97.57%. The fabrication process is carried out using MITS 11 Autolab fabrication machine with the low cost FR4 substrate and verified the performance improvement of the developed filter.

Analysis of Second Order Filter in Remote Laboratory

In this paper, performance analysis of second order analog filters using Remote Laboratory is presented. The Remote laboratory system developed indigenously has the many analog experiments that can be conducted by authorized user from anywhere at any time. The remote laboratory system also has second order Low pass filter (LPF) and High pass filter (HPF). It possible to perform filter experiments with three different values of resistors, two capacitors with different values. Along with this there is option of modifying the voltage gain of the filter. This will enable the user to analyze the filter performances thoroughly. Both time and frequency response are obtained to determine pass band gain, pole and zero locations and the roll-off the filter. Using this user can know the effect of voltage gain on the circuit and obtain maximally flat response also. Remote laboratory system for filters is built using an ingeniously developed PCB and uses Arduino board for selecting and switching experiments and Analog Discovery a product ot National Instruments is used for applying and measuring the signals during the conduction of experiments. The user has the freedom in applying signals of desired signals. Paper also presents typical analysis report of filters conducted remotely.

Miniaturised LTCC diplexer with low insertion loss for LTE application

A novel multilayer diplexer with low insertion loss and high selectivity for long-term evolution (LTE) application is proposed through the combination of two quasi-lumped element filters. Based on the equivalent circuit of the diplexer, the locations of the transmission zeros can be adjusted separately by changing the component value of each channel, thus high isolation level and wide stopband can be achieved simultaneously. Furthermore, the diplexer has an extremely compact size of 1.6 mm × 0.8 mm × 0.5 mm by using low temperature co-fired ceramic (LTCC) multilayer technology.

On the Zeros of Ramanujan Filters

Ramanujan filter banks have been used for identifying periodicity structure in streaming data. This letter studies the locations of zeros of Ramanujan filters. All the zeros of Ramanujan filters are shown to lie on or inside the unit circle in the $z$ -plane. A convenient factorization appears as a corollary of this result, which is useful to identify common factors between different Ramanujan filters in a filter bank. For certain families of Ramanujan filters, further structure is identified in the locations of zeros of those filters. It is shown that increasing the number of periods of Ramanujan sums in the filter definition only increases zeros on the unit circle in $z$ -plane. A potential application of these results is that by identifying common factors between Ramanujan filters, one can obtain efficient implementations of Ramanujan filter banks (RFB) as demonstrated here.

New negative coupling structure and its application on substrate integrated waveguide bandpass filters

To design cross-coupled substrate integrated waveguide (SIW) bandpass filters (BPFs) with high performance, a new negative coupling structure is proposed, which is constructed by two coupled lines with shorted ends. The negative coupling structure is analyzed in detail. The stracture which can realize both relatively weak and strong negative coupling strength. The optimization method based on characteristic polynomials and reference zeros and poles of scattering parameters is realized for the filter design. To verify the proposed negative coupling structure, two fourth-order cross-coupled SIW BPFs with the center frequency of 10 GHz based on the optimized coupling matrixes are designed. The first one has a normalized bandwidth of 3% with a negative coupling in one cross-coupling path to illustrate the realization of weak negative coupling strength, and the second one has a normalized bandwidth of 8% with a negative coupling in one main coupling path to illustrate the realization of strong negative coupling strength. Finally, the two BPFs are fabricated and measured. Simulation and measurement results are in good agreement, which demonstrates the feasibility of the proposed negative coupling structure and its application on cross-coupled SIW filters with high performance. The influence of weak disperse cross coupling on locations of transmission zeros is also discussed.

The location of critical points of polynomials

Given a set of points in the complex plane, an incomplete polynomial is defined as one which has these points as zeros except one of them. Recently, the classical result known as Gauss–Lucas theorem on the location of zeros of polynomials and their derivatives was extended to the linear combinations of incomplete polynomials. In this paper, a simple proof of this result is given, and some results concerning the critical points of polynomials due to Jensen and others have extended the linear combinations of incomplete polynomials.

Location of zeros for the partition function of the Ising model on bounded degree graphs

The seminal Lee-Yang theorem states that for any graph the zeros of the partition function of the ferromagnetic Ising model lie on the unit circle in $\mathbb C$. In fact the union of the zeros of all graphs is dense on the unit circle. In this paper we study the location of the zeros for the class of graphs of bounded maximum degree $d\geq 3$, both in the ferromagnetic and the anti-ferromagnetic case. We determine the location exactly as a function of the inverse temperature and the degree $d$. An important step in our approach is to translate to the setting of complex dynamics and analyze a dynamical system that is naturally associated to the partition function.

English

English

Complex Variable Theorems for Finding Zeroes and Poles of Transcendental Functions

The principle of the argument or the winding number is useful in finding the number of zeros of an analytic function in a given contour. A simple extension of this theorem yields relationships involving the locations of these zeros! The resulting equations can be solved very accurately for the zero locations, thus avoiding initial, guess values, which are required by many other techniques. Examples such as a 20th order polynomial, natural frequencies of a thin wire will be discussed.

Selectivity improved directional filters using cross-coupling introduced transmission zeros

ABSTRACTIn this paper, the realization of traveling-wave directional filters allowing for selectivity improvement without increasing filter’s order is presented and studied. It is shown that the introduction of loose cross-coupling between #(n-1)th loop resonator and isolated port of the nth-order directional filter allows for generating transmission zeros in the bandpass branch and thus to improve the filter`s roll-off. Moreover, the electrical length of the cross-coupling connecting transmission line allows for adjusting the location of transmission zeros and realizing symmetric or asymmetric frequency response. The presented approach is theoretically analyzed and experimentally verified. Exemplary second- and third-order directional filters with symmetrically placed transmission zeros were designed to operate at f0 = 1 GHz, manufactured and measured. The obtained results prove their applicability towards the realization of frequency multiplexers.

Partially Air-Filled Substrate Integrated Waveguide Filters With Full Control of Transmission Zeros

This paper presents the investigation and testing of novel substrate integrated waveguide (SIW) bandpass filters, based on air-filled cavity resonators. Removing the lateral parts of the dielectric substrate in SIW rectangular cavities enables the use of the TM120 and TM210 modes to implement a dual-mode resonator. In addition, the fundamental TM110cavity mode is adopted to implement a transmission zero. This paper demonstrates the complete control of the central operation frequency, the pass bandwidth, the spurious-free bandwidth region, and the location of the transmission zeros. After a comprehensive theoretical investigation, design rules are derived and applied to the implementation of a variety of dual-mode cavities, which have been manufactured and tested. Moreover, these basic structures have been used as building blocks to design higher order filters: simulations and measurements of four-pole filters are reported for validation.

Measuring complex-partition-function zeros of Ising models in quantum simulators

Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex partition function zeroes of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates, local spin rotations, and projective measurements along two orthogonal quantization axes. Besides presenting numerical simulations of the measurement outcomes for an exemplary classical model, we discuss the effect of projection noise and the feasibility of the implementation on state of the art platforms for quantum simulation.