The Series of Reciprocals of Non-central Binomial Coefficients

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.

Two Kinds of Series Involving the Reciprocals of Binomial Coefficients

By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.

On the Sum of Reciprocals of Mersenne Primes

The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.

ON APPROXIMATION BY RECIPROCALS OF POLYNOMIALS WITH POSITIVE COEFFICIENTS IN ORLICZ SPACES

This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients

Summation of Reciprocals Related to Square of Products of Fibonacci Numbers

By applying the method of on summation by parts,the purpose of this paper is to give several reciprocal summations related to squares of products of the Fibonacci numbers.

On Approximation by Reciprocals of Spherical Harmonics in L^p Norm

Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.

Nonreciprocal Photon Blockade Based on Zeeman Splittings Induced by a Fictitious Magnetic Field

Quantum nonreciprocity, such as nonreciprocal photon blockade, has attracted a great deal of attention due to its unique applications in quantum information processing. Its implementation primarily relies on rotating nonlinear systems, based on the Sagnac effect. Here, we propose an all-optical approach to achieve nonreciprocal photon blockade in an on-chip microring resonator coupled to a V-type Rb atom, which arises from the Zeeman splittings of the atomic hyperfine sublevels induced by the fictitious magnetic field of a circularly polarized control laser. The system manifests single-photon blockade or multi-photon tunneling when driven from opposite directions. This nonreciprocity results from the directional detunings between the countercirculating probe fields and the V-type atom, which does not require the mechanical rotation and facilitates integration. Our work opens up a new route to achieve on-chip integrable quantum nonreciprocity, enabling applications in chiral quantum technologies.

Reversible Optical Isolators and Quasi-Circulators Using a Magneto-Optical Fabry-Pérot Cavity

Nonreciprocal optical devices are essential for laser protection,modern optical communication and quantum information processing by enforcing one-way light propagation.The conventional Faraday magneto-optical nonreciprocal devices rely on a strong magnetic field,which is provided by a permanent magnet.As a result,the isolation direction of such devices is fixed and severely restricts their applications in quantum networks.In this work,we experimentally demonstrate the simultaneous one-way transmission and unidirectional reflection by using a magneto-optical Fabry-Pérot cavity and a magnetic field strength of 50 mT.An optical isolator and a three-port quasi-circulator are realized based on this nonreciprocal cavity system.The isolator achieves an isolation ratio of up to 22 dB and an averaged insertion loss down to 0.97 dB.The quasi-circulator is realized with a fidelity exceeding 99% and an overall survival probability of 89.9%,corresponding to an insertion loss of~0.46 dB.The magnetic field is provided by an electromagnetic coil,thereby allowing for reversing the light circulating path.The reversible quasi-circulator paves the way for building reconfigurable quantum networks.

Magnetic Nonreciprocity in a Hybrid Device of Asymmetric Artificial Spin-Ice-Superconductors

Controlling the size and distribution of potential barriers within a medium of interacting particles can unveil unique collective behaviors and innovative functionalities.We introduce a unique superconducting hybrid device using a novel artificial spin ice structure composed of asymmetric nanomagnets.This structure forms a distinctive superconducting pinning potential that steers unconventional motion of superconducting vortices,thereby inducing a magnetic nonreciprocal effect,in contrast to the electric nonreciprocal effect commonly observed in superconducting diodes.Furthermore,the polarity of the magnetic nonreciprocity is in situ reversible through the tunable magnetic patterns of artificial spin ice.Our findings demonstrate that artificial spin ice not only precisely modulates superconducting characteristics but also opens the door to novel functionalities,offering a groundbreaking paradigm for superconducting electronics.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Bidirectional rotating direct-current triboelectric nanogenerator with self-adaptive mechanical switching for harvesting reciprocating motion

Amid the growing interest in triboelectric nanogenerators(TENGs)as novel energy-harvesting devices,several studies have focused on direct current(DC)TENGs to generate a stable DC output for operating electronic devices.However,owing to the working mechanisms of conventional DC TENGs,generating a stable DC output from reciprocating motion remains a challenge.Accordingly,we propose a bidirectional rotating DC TENG(BiR-TENG),which can generate DC outputs,regardless of the direction of rotation,from reciprocating motions.The distinct design of the BiR-TENG enables the mechanical rectification of the alternating current output into a rotational-direction-dependent DC output.Furthermore,it allows the conversion of the rotational-direction-dependent DC output into a unidirectional DC output by adapting the configurations depending on the rotational direction.Owing to these tailored design strategies and subsequent optimizations,the BiR-TENG could generate an effective unidirectional DC output.Applications of the BiR-TENG for the reciprocating motions of swinging doors and waves were demonstrated by harnessing this output.This study demonstrates the potential of the BiR-TENG design strategy as an effective and versatile solution for energy harvesting from reciprocating motions,highlighting the suitability of DC outputs as an energy source for electronic devices.

Reciprocal Distance Laplacian Eigenvalue Distribution Based on Graph Parameters

Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.

2种机用镍钛器械在乳磨牙根管治疗中的临床效果观察

目的探讨Reciproc机用镍钛器械和Protaper机用镍钛器械在乳磨牙根管治疗中的临床应用效果。方法选取2020年1月—2021年1月甘肃中医药大学附属医院口腔科就诊的乳牙牙髓病患儿50例,分别用Reciproc镍钛器械(RE组)和Protaper镍钛器械(PT组)进行根管治疗。分别记录2组的根管预备时间、诊间疼痛评估值和术后X线片检查充填效果。所有的根管治疗操作均为同一医生进行。结果平均每根根管预备时间RE组为(3.70±1.19)min,PT组为(5.43±1.16)min,RE组的预备时间短于PT组,差异有统计学意义(P<0.05)。2组约诊间痛评分和根管充填效果比较,差异无统计学意义(P>0.05)。结论机用镍钛器械Protaper和Reciproc在乳牙根管治疗时具有预备时间短、诊间疼痛反应低、充填效果佳的优点,其中Reciproc在治疗操作时间方面优于Protaper。

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

Inverse Electromagnetic Scattering by a Penetrable Chiral Object

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.

新型往复运动单支锉根管预备对牙本质微裂的影响

目的 :比较新一代往复运动单支锉WaveOne Gold和Reciproc Blue与上一代WaveOne和Reciproc在根管预备后产生牙本质微裂的差异。方法:将90颗离体下颌单根前磨牙随机分为6组(n=15),分别为手用K锉组、WaveOne组、Reciproc组、WaveOne Gold组、Reciproc Blue组和空白对照组。将实验组根管预备至25#,空白对照组不作预备。利用硬组织切片机在距根尖孔3、6和9 mm处水平切割牙根,体视显微镜下放大25倍,观察不同横截面牙本质微裂情况。采用SPSS 17.0软件包对数据进行统计学分析。结果:手用K锉组和空白对照组未发现牙本质微裂;实验组中,WaveOne、WaveOne Gold、Reciproc和Reciproc Blue在根管预备后均产生了牙本质微裂,其中,WaveOne和手用K锉组产生的牙本质微裂纹数目差异有统计学意义(P<0.05),裂纹主要集中于根管根中段;Reciproc和Reciproc Blue 2种往复运动单支锉造成的牙本质微裂数目相同,与对照组相比无统计学差异。结论:使用新一代往复运动单支锉WaveOne Gold和Reciproc Blue不会增加根管预备后牙本质微裂纹发生的风险。

Reciproc单支锉清除iRoot SP糊剂单尖法根管充填材料的再治疗效率研究

目的以AH糊剂冷侧压法、热牙胶垂直加压法为对照,口腔锥形束CT(CBCT)三维重建评价使用Reciproc单支锉去除iRoot SP糊剂单尖法术后根管充填材料的再治疗效率。方法选择福建医科大学附属福州市第一医院口腔科2021年7—11月正畸拔除的卵圆形单根管下颌前磨牙90个,采用随机数表法分为iRoot SP糊剂单尖法组(1组)、热牙胶垂直加压组(2组)和AH糊剂冷侧压组(3组)。使用Reciproc单支锉再治疗,终末超声荡洗2 min。分别于根充术后、再治疗、超声荡洗后CBCT扫描并三维重建,记录再治疗时间、根管残余充填材料体积。结果1组再治疗耗时最长,2组最短,差异有统计学意义(P<0.05)。1组残余充填材料最多,大于2组,差异有统计学意义(P<0.05),大于3组,但差异无统计学意义(P>0.05)。超声荡洗后,1组残余量大幅度减少,差异有统计学意义(P<0.05);最终残余量大于2组,差异有统计学意义(P<0.05),大于3组,但差异无统计学意义(P>0.05)。结论无论哪种充填方法,Reciproc单支锉再治疗均不能完全去除充填材料。iRoot SP糊剂单尖法进行再治疗耗时最多,残余量也最多,超声荡洗能够显著减少残余量。

Relaxed Stability Criteria for Delayed Generalized Neural Networks via a Novel Reciprocally Convex Combination

Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the proposed novel reciprocally convex method leads to a tight bound for integral inequality combination and encompasses several existing approaches as special cases.

A Quorum Sensing Active Matter in a Confined Geometry

Inspired by the problem of biofilm growth,we numerically investigate clustering in a two-dimensional suspension of active(Janus)particles of finite size confined in a circular cavity.Their dynamics is regulated by a non-reciprocal mechanism that causes them to switch from active to passive above a certain threshold of the perceived near-neighbor density(quorum sensing).A variety of cluster phases,i.e.,glassy,solid(hexatic)and liquid,are observed,depending on the particle dynamics at the boundary,the quorum sensing range,and the level of noise.

三种镍钛机用单支锉预备不同弯曲根管的体外研究

目的 比较三种镍钛机用单支锉在离体牙不同弯曲根管中的预备效果.方法 收集2021年1月至2022年8月符合实验标准的上下颌离体前磨牙120颗,根据弯曲程度分为I类、II类2组,分别使用Waveone gold(WOG),Reciproc blue(RPB),M3-L进行根管预备,通过预备前后根管CBCT影像对比,从根管预备时间、工作长度变化值、根尖偏移、角度差及器械抗疲劳能力等方面比较三种镍钛机用单支锉的根管成形能力.结果 M3-L根管预备时间I类(31.9±1.5)s、II类(34.6±1.9)s,WOG为(30.5±1.9)s与(32.8±2.6)s,RPB为(29.8±1.3)s与(30.7±2.5)s,三组差异有统计学意义(P<0.05);预备后根管角度差中M3-L I类为(0.656±0.425),II类为(0.832±0.366),WOG为(1.461±0.645)与(1.529±0.850),RPB为(1.328±0.399)与(1.398±0.532),差异有统计学意义(P<0.05);根尖偏移量与工作长度变化值三组比较,差异无统计学意义(P>0.05);M3-L最早发生器械形变(在预备至10个根管时发生),WOG与RPB分别在14与15个根管时发生器械形变,三者均未发生折断现象.结论 在预备弯曲度≤20°的离体牙根管中,M3-L与RPB、WOG均可以获得良好的根管预备效果,其中M3-L根管预备时间最长,预备后根管角度差值最小.