symmetry

摘要： Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number;As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.

摘要： In recent years, the properties of parity-time(PT) symmetric system are revealed to realize plenty of counterintuitive phenomena[1]. In particular, encircling the exceptional point(EP) in a PT symmetric system for asymmetric mode switching has caught people’s eyes because of its potential in the design of chiral devices.

摘要： Using translation β = σ −1/2 and rotation s =σ + it = 1/2 + iz, z = t −iβ, Riemann got two results: (Theorem A) the functional equation ξ(z) = G(s)ξ(s), where , and (Theorem B) the product expression , where zj are all roots of ξ(z), including complex roots. He proposed Riemann conjecture (RC): All roots of ξ(z) are real. As the product expression can only be used as a tool of contradiction, we prove RC by contradiction. To avoid the zeros of ξ(1/2 + it), define a subset . We have basic estimate , on L (R). One can construct by all real roots tj of ξ(t). If ξ has no complex roots, then w(t) = G(s)ξ(s) for s = 1/2 + it. If the product expression has a complex root z'=t' −iα, where 0 a ≤ 1/2, R' = |z′| > 10, then ξ(z) has four complex roots ±(t′ ± iα), and should contain fourth order factor p(z), i.e. ξ(z) = w(z)p(z). But p(z) can not be contained in ξ(s), as we have on L(R) and p(t) ≥ 0.5(t/R)4 . As a result, we can rewrite ξ(t) = w(t)p(t) =G(s)ξ(s)p(t) on and get This contradicts the basic estimate. Therefore ξ(z) has no complex roots and RC holds.

摘要： Ancient poetry represents historical and cultural legacies accumulated by the Chinese nation for thousands of years and underpins the strong cultural confidence of the Chinese people.Tang poetry distinguishes itself from other literary works with its beautiful rhyme and symmetry.Previous studies of English translations of Tang poetry mostly focused on appreciation,analysis,and critics of different translation versions.Few researchers have delved into the specific translation methods for achieving the rhyming and symmetrical effects of Tang poetry in the target text.This paper examined Professor Xu Yuanchong’s English translation of 300 Tang Poems as the research object,and elaborated on how to retain the rhyming and symmetrical effects of Tang poems.This paper also summarized some practical methods that can be applied to translating Tang poems.Rhyming can be realized by the addition of end rhyme words and changes in word or line order.Symmetry can be achieved by the omission of a modifier or predicate,the addition of function words,changes in word order,or parallelism with the original sentence structure.

摘要： The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.

摘要： We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu),p>1,θ>−p,and T is a half-space{x_(1)>0}.When λ>Θ(where Θ is the Hardy constant),we show that under suitable conditions on f andθ,the equation has a unique positive solution.Moreover,the exact behavior of the unique positive solution as x_(1)→0^(+),and the symmetric property of the positive solution are obtained.

摘要： Intrinsic magnetic topological materials,namely the stoichiometric magnetic compounds possessing both inherent magnetic order and topological electronic states,have attracted tremendous interest in the research of condensed matter physics and materials science[1].Such materials not only bring new opportunities to realize many exotic topological phenomena under time-reversal symmetry breaking,but also show great potential in applications of quantum technology[2].

摘要： Intrinsic magnetic topological materials,namely the stoichiometric magnetic compounds possessing both inherent magnetic order and topological electronic states,have attracted tremendous interest in the research of condensed matter physics and materials science[1].Such materials not only bring new opportunities to realize many exotic topological phenomena under time-reversal symmetry breaking,but also show great potential in applications of quantum technology[2].

摘要： The pairing symmetry of the superconducting order parameter contains key information about the pairing mechanism of the superconductor. For conventional superconductors, whose pairing is usually induced by the electron-phonon interaction, the pairing symmetry is s-wave, and the superconducting gap is fully open everywhere on the Fermi surface. For unconventional superconductors such as the cuprate and heavy fermion superconductors, other pairing symmetries may occur, leading to symmetry-mandated nodes in the superconducting order parameter.

摘要： Metasurfaces are planar arrays composed of artificial nanostructures at the subwavelength scale.Since the first demonstration of their excellent capacity in the phase manipulation of optical waves,metasurfaces have attracted increasing attention in optics and other disciplines,with extraordinary progress over the past decade.The unique capabilities of metasurfaces in the multidimensional manipulation of optical waves have made them versatile and powerful platforms for integrating and minimizing optical devices[1,2].

摘要： Lattice symmetry控制电路电子开关，涉及信号输入电路串接驱动电路串接开关电路串接滤波电路构成的电子开关。开关电路由IGBT1和IGBT2发射极EA和EB对接构成Lattice symmetry开关控制电路，IGBT1管的CA脚与IGBT2管的CB脚之间的C1、RA1和C2、RA2构成正弦波交替信号调整电路，IGBT1管的CA脚与IGBT2管的CB脚之间并接由C3串接RA3构成的正弦波保真电路。IGBT1管的EA和IGBT2的EB对接点和RA1和C2之间的连接点接通。驱动电路芯片为FAN8800。滤波电路采用EMI标准电子滤波器。