Integer Research Articles

Enhancement of the magneto-electronic properties by GGA and TB-mBJ approaches for KMgO3 perovskite oxide

We investigate the structural, elastic, electronic and magnetic properties of KMgO3. First-principal calculations, based on the formalism of the density functional theory (DFT) and the method of full potential augmented and linearized plane waves (FP-LAPW) implemented in the Wien2k code. The exchange and correlation effects were treated by the following two approximations: generalized gradient approximation (GGA) and Tran-Blaha modified beck Johnson (TB-mBJ) potentials. After analyzing the obtained structural parameters, the results revealed that KMgO3compound is most stable in its ferromagnetic configuration. The formation energy value showed that this compound can be experimentally synthesized. Furthermore, the calculated band structures, and density of states (DOSs) indicate the half-metallic behavior of KMgO3. We found also that the total magnetic moment is an integer value of 3μBwhich confirms the half-metallic character. The magnetic moment specially issues from the spin-polarization of p electrons of O atoms.

Finding large additive and multiplicative Sidon sets in sets of integers

AbstractGiven $$h,g \in {\mathbb {N}}$$ h , g ∈ N , we write a set $$X \subset {\mathbb {Z}}$$ X ⊂ Z to be a $$B_{h}^{+}[g]$$ B h + [ g ] set if for any $$n \in {\mathbb {Z}}$$ n ∈ Z , the number of solutions to the additive equation $$n = x_1 + \dots + x_h$$ n = x 1 + ⋯ + x h with $$x_1, \dots , x_h \in X$$ x 1 , ⋯ , x h ∈ X is at most g, where we consider two such solutions to be the same if they differ only in the ordering of the summands. We define a multiplicative $$B_{h}^{\times }[g]$$ B h × [ g ] set analogously. In this paper, we prove, amongst other results, that there exist absolute constants $$g \in {\mathbb {N}}$$ g ∈ N and $$\delta >0$$ δ > 0 such that for any $$h \in {\mathbb {N}}$$ h ∈ N and for any finite set A of integers, the largest $$B_{h}^{+}[g]$$ B h + [ g ] set B inside A and the largest $$B_{h}^{\times }[g]$$ B h × [ g ] set C inside A satisfy $$\begin{aligned} \max \{ |B|, |C| \} \gg _{h} |A|^{(1+ \delta )/h }. \end{aligned}$$ max { | B | , | C | } ≫ h | A | ( 1 + δ ) / h . In fact, when $$h=2$$ h = 2 , we may set $$g = 31$$ g = 31 , and when h is sufficiently large, we may set $$g = 1$$ g = 1 and $$\delta \gg (\log \log h)^{1/2 - o(1)}$$ δ ≫ ( log log h ) 1 / 2 - o ( 1 ) . The former makes progress towards a recent conjecture of Klurman–Pohoata and quantitatively strengthens previous work of Shkredov.

The covariety of numerical semigroups with fixed Frobenius number

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Maldistributed sequences in metric spaces

Let a kind of measure μ be given on the set of all positive integers N. By a μ-maldistributed sequence in a metric space (X,d) we mean any sequence possessing μ-extremely many points in each nonempty open subspace of (X,d). Let s(X) denote the metric space of all sequences in (X,d) endowed with the Fréchet metric. In this paper we study topological properties of the set of all maldistributed sequences in X as a subspace s(X). We show that if (X,d) is separable then this set is residual for a large class of commonly used measures μ on N.

Application of Matrix in Engineering

Mathematics plays importance role in our daily life. Branch of Mathematics are as given, Real analysis, vector analysis, group theory, linear algebra, vector algebra, ordinary differential calculus, integration, discrete mathematics, Matrices and determinant etc. Throughout time, matrix have played a crucial role in solving sets of linear equations. In branch of applied mathematics & many branches of applied science matrix are used. We can check the outcome of a matrix in MATLAB to see the images created by computers. In physics, optics, which is the science of light, used matrices even before they were used in computer - generated images. In applied mathematics, matrices have diverse applications, Such as signal processing, image processing and more. For instance, in graph theory, matrices help represent connections between nodes, with the integer values in an adjacency matrix indicating the number of connections a particular node possesses.

ZEROS OF PARTITION FUNCTION FOR Z5-SYMMETRIC MODEL ON SQUARE LATTICE-PARTICULAR CASE

We study a statistical mechanics model of multiple-phase transitions called the ZQ-symmetric model on the square lattice for five possible spin directions (Q = 5). This study aims to investigate the existence of phase transition(s) and discuss the distribution of partition function zeros on the complex-temperature plane. Some cases of energy list χ are considered where they are written in an arbitrary arrangement of integer numbers (usually in decreasing value due to the angle of separation). The partition functions are computed using a transfer matrix approach, and their zeros are found numerically using the NewtonRaphson method. A Monte-Carlo Metropolis simulation is then performed to study the critical point of phase transition. The results are compared to the zeros distribution of the partition functions for the considered cases. Studying this generalised model is vital to mimic the system in the real world and to help experimental works use a more sustainable approach.

A Review of Brahmagupta's Contributions

The life, accomplishments, and legacy of prominent Indian mathematician and astronomer Brahmagupta from the 7th century are examined in this review. Brahmagupta, who is well-known for his contributions to algebra, arithmetic, and astronomy, provided ground-breaking ideas in his "Brāhmasphuṭasiddhānta,"a foundational work that included the rules for mathematical operations involving zero and negative integers. His efforts established the groundwork for contemporary mathematics, inspiring other researchers in mediaeval Europe as well as the Islamic world. In order to emphasize Brahmagupta's methods, his contribution to the advancement of mathematical thought, and the ongoing influence of his work on current mathematical practices, this review synthesizes historical accounts and contemporary interpretations.

Graph realization of sets of integers

Graph theory is used in many areas of chemical sciences, especially in molecular chemistry. It is particularly useful in the structural analysis of chemical compounds and in modeling chemical reactions. One of its applications concerns determining the structural formula of a chemical compound. This can be modeled as a variant of the well-known graph realization problem. In the classical version of the problem, a sequence of natural numbers is given, and the question is whether there exists a graph in which the vertices have degrees equal to the given numbers. In the variant considered in this paper, instead of a sequence of natural numbers, a sequence of sets of natural numbers is given, and the question is whether there exists a multigraph such that each of its vertices has a degree equal to a number from one of the sets. This variant of the graph realization problem matches the nature of the problem of determining the structural formula of a chemical compound better than other variants considered in the literature. We propose a polynomial time exact algorithm solving this variant of the problem.

Two problems on subset sums

For a set A of positive integers, let P(A) denote the set of all finite subset sums of A. In this paper, we completely solve a problem of Chen and Wu by proving that if B={b1<b2<⋯} is a sequence of integers with b1≥11, 3b1+5≤b2≤4b1, 3b2+2≤b3≤3b2+b1 and 3bn−bn−2≤bn+1≤3bn(n≥3), then there exists a set of positive integers A for which P(A)=N∖B. We also partially answer a problem of Wu by determining the structure of B={b1<b2<⋯} with b1>10 and b2>3b1+4, for which there exists a set of positive integers A such that P(A∩[0,bk])=[0,2bk]∖{bi,2bk−bi:1≤i≤k}(k≥2).

Generalization of the Distance Fibonacci Sequences

In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators for these sequences and offered a graphical representation to clarify their structure. Furthermore, we demonstrated how these generalizations can be applied to obtain the Padovan and Narayana sequences for specific parameter values.

Chess Game Rook‐Icon Movement‐Based Photovoltaic Array Reconfiguration for Higher Shade Dispersion and Improved Global Power Peaks Under Partial Shading Conditions: An Experimental Study

Solar photovoltaic (PV) system generates low power because of nonuniform sun irradiation compared to standard test conditions. Partial shading conditions (PSCs) can arise from various factors, with passing clouds, trees, telecommunication towers, bird droppings, and similar elements being among the most prevalent causes. Under the shading scenario, multiple global and local maxima power points exist on the P–V curves. Herein, the chess game rules for the “Rook” icon are followed to attain the optimal placement of integer numbers (1–9) in the 9 × 9 size game puzzle matrix. The integer number‐based game puzzles such as Su‐Do‐Ku, symmetric matrix, and proposed Rook's movement‐game theory (RMGT) to rearrange the PV modules in arrays are investigated and compared with the standard arrangements such as series‐parallel, total‐cross‐tied during PSCs. The suggested RMGT puzzle‐based arrangement is able to achieve higher power at global maximum power point, performance enhancement, fill factor, and low power loss. As a result, the experimental study proves the superiority of RMGT configuration compared to conventional methodologies under the shading scenarios. The proposed RMGT‐based PV array is tested and obtained the performance higher side as, , , , and compared to existing reconfiguration methodologies.

Bernstein–Jacobi-type operators preserving derivatives

A general frame for Bernstein-type operators that preserve derivatives is given. We introduce Bernstein-type operators based in the weighted classical Jacobi inner product on the interval [0, 1] that extend the well known Bernstein–Durrmeyer operator as well as some other types of Bernstein operators that appear in the literature. Apart from standard results, we deduce properties about the preservation of derivatives and prove that classical Jacobi orthogonal polynomials on [0, 1] are the eigenfunctions of these operators. We also study the limit cases when one of the parameters of the Jacobi polynomials is a negative integer. Finally, we study several numerical examples.

On a sumset problem for dilated integer sets

Let [Formula: see text] be a non-empty finite set of integers. For any integer [Formula: see text], let [Formula: see text]. One of the important problems in additive combinatorics is to find the optimal lower bound for the cardinality of the sumset [Formula: see text]. Cilleruelo, Silva, and Vinuesa conjectured that, if [Formula: see text] is a positive integer and [Formula: see text] is a finite set of integers with sufficiently large cardinality, then [Formula: see text]. For some values of [Formula: see text] this conjecture is already confirmed. In this article, under certain restrictions on set [Formula: see text], we confirm this conjecture for all positive integers [Formula: see text] except for those of the form [Formula: see text] or [Formula: see text] where [Formula: see text] is an odd prime number and [Formula: see text] for [Formula: see text].

From cavitation to astrophysics: Explicit solution of the spherical collapse equation.

Differential equationsof the form R[over ̈]=-kR^{γ}, with a positive constant k and real parameter γ, are fundamental in describing phenomena such as the spherical gravitational collapse (γ=-2), the implosion of cavitation bubbles (γ=-4), and the orbital decay in binary black holes (γ=-7). While explicit elemental solutions exist for select integer values of γ, more comprehensive solutions encompassing larger subsets of γ have been independently developed in hydrostatics (see Lane-Emden equation) and hydrodynamics (see Rayleigh-Plesset equation). I here present a universal explicit solution for all real γ, invoking the beta distribution. Although standard numerical ordinary differential equationsolvers can readily evaluate more general second-order differential equations, this explicit solution reveals a hidden connection between collapse motions and probability theory that enables further analytical manipulations, it conceptually unifies distinct fields, and it offers insights into symmetry properties, thereby enhancing our understanding of these pervasive differential equations.

Effect of shape anisotropy on percolation of aligned and overlapping objects on lattices.

We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences regarding the percolation behavior of anisotropic shapes. We consider a prototypical anisotropic shape-rectangle-on a square lattice and show that, for rectangles of width unity (sticks), the percolation threshold is a monotonically decreasing function of the stick length, whereas, for rectangles of width greater than two, it is a monotonically increasing function. Interestingly, for rectangles of width two, the percolation threshold is independent of its length. We show that this independence of threshold on the length of a side holds for d-dimensional hypercubiods as well as for specific integer values for the lengths of the remaining sides. The limiting case of the length of the rectangles going to infinity shows that the limiting threshold value is finite and depends upon the width of the rectangle. This "continuum" limit with the lattice spacing tending to zero only along a subset of the possible directions in d dimensions results in a "semicontinuum" percolation system. We show that similar results hold for other anisotropic shapes and lattices in different dimensions. The critical properties of the aligned and overlapping rectangles are evaluated using Monte Carlo simulations. We find that the threshold values given by the lattice-excluded volume theory are in good agreement with the simulation results, especially for larger rectangles. We verify the isotropy of the percolation threshold and also compare our results with models where rectangles of mixed orientation are allowed. Our simulation results show that alignment increases the percolation threshold. The calculation of critical exponents places the model in the standard percolation universality class. Our results show that shape anisotropy of the aligned, overlapping percolating units has a marked influence on the percolation properties, especially when a subset of the dimensions of the percolation units is made to diverge.

Temperature and pressure dependencies of Sm valence in SmB[formula omitted] Kondo insulator probed by x-ray absorption spectroscopy

Pressure and temperature induced valence changes in the Kondo insulator SmB6 have been investigated using x-ray absorption spectroscopy (XAS) along several isobaric cooling runs and one isothermal compression. The average valence of Sm at various pressure and temperature conditions is extracted from high quality XAS data by peak fitting procedures. The temperature dependence of the Sm valence at ambient pressure shows changes of slope near the known characteristic temperatures of gap formation (120 K) and the in-gap state (50 K). At higher pressures the average valence also shows similar temperature dependent trends upon cooling but the slope changes are less pronounced. This behavior is discussed in relation to the possible existence of an underlying first order valence transition and its critical end point. At constant temperature (T=20 K), the Sm valence increases rapidly with pressure; however, it remains far below the expected integer value (3+) near the onset of the magnetic ordering and gap closure. In addition, the local structure of SmB6 at ambient conditions has been analyzed using extended x-ray absorption fine structure.

On a unified approach to homogeneous second-order linear difference equations with constant coefficients and some applications

AbstractIn this article, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of this type such as the Fibonacci and Lucas sequences. Next, we show the main advantage of our formula which is based on the fact that future calculations rely on the previous ones and this is true from any desired starting point. As applications, we show that Binet’s formula, in this case, is valid for negative integers as well. Finally, new summation formulas relating elements of such sequences. As a conclusion, we present a formula for the sum of squares of Chebychev polynomials of the first and second kind.

Higher-order beyond-band discrete solitons in binary waveguide arrays

We study higher-order beyond-band discrete solitons (HOBBDSs) and quasi-HOBBDSs, which can be constructed by multiplying the solutions of fundamental single-peaked beyond-band discrete solitons by a soliton order parameter larger than unity. In the quasi-continuous regime when the HOBBDS peak amplitude is low (thus its width is large) and the soliton order parameter is a small integer number, HOBBDSs periodically evolve during propagation and their dynamics are similar to those of higher-order solitons governed by the nonlinear Schrödinger equation in an optical fiber, including the periodicity, pattern evolution, and independence of the period length on the soliton order parameter. If the soliton order parameter is still small but not an integer, then one can obtain the quasi-HOBBDSs whose profiles almost periodically evolve during propagation. The breathing length of quasi-HOBBDSs decreases if the soliton order parameter increases. Moreover, the breathing length of quasi-HOBBDSs is approximately inversely proportional to the square values of the peak amplitude of the fundamental beyond-band discrete solitons, just like what happens with the period length of the higher-order solitons governed by the nonlinear Schrödinger equation. If the fundamental beyond-band discrete solitons are intense enough and/or the soliton order parameter is large enough, then most of the energy of the beams is eventually trapped in a single waveguide.

Oscillations of Fourier coefficients over the sparse set of integers

Oscillations of Fourier coefficients over the sparse set of integers

HJ Semi Symmetric Cryptographic Algorithm

This paper presents an algorithm for performing encryption and decryption using modular exponentiation mainly based on Euler’s Theorem. The algorithm uses the properties of modular arithmetic to ensure secure communication. The gcd function is employed to find coprime numbers within a given range, which are then utilized as bases for encryption and decryption. The modular Exponentiation function efficiently computes the exponentiation of a base to a power modulo a given modulus. Through a step-by-step process, the algorithm encrypts a numerical message using the selected base and then decrypts it, ensuring the original message is recovered accurately. Experimental results demonstrate the effectiveness and reliability of the algorithm for secure data transmission. In the conclusion we discussed the effectiveness of the algorithm compared to the existing ones such as Elgamal algorithm and RSA Cryptography. The algorithm presented in this paper publishes only the modulus (integer) number and protocols of key exchanges kept secret between sender and receiver; therefore, the algorithm is not fully asymmetric but semi symmetric.