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In recent years, noise barriers are considered as one of the main ways to control traffic noise pollution. In this study, two different types of noise barriers: the parallel barrier model with primitive root diffuser (PP) and the parallel barrier model with quadratic residue diffuser (PQ) were designed, and the two-dimensional boundary element method was used to predict their efficacy in noise control. The results of this research compared the improvement in performance of parallel barriers covered with the primitive root diffuser (PRD) with parallel barriers covered with the quadratic residue diffuser (QRD) and the simple parallel barriers (P). Efficacy in different frequencies, using the diffuser with different depths based on the PP model was studied and was compared to the PQ barrier and a reference barrier (P) without any wells. The results showed that the efficacy of the parallel sound barrier arm covered by PRD in different intended receiver positions was higher than QRD and the simple parallel sound barrier arm. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops the residue harmonic balance solution procedure to predict the bifurcated periodic solutions of some autonomous delay differential systems at and after Hopf bifurcation. In this solution procedure, the zeroth-order solution employs just one Fourier term. The unbalanced residues due to Fourier truncation are considered by solving linear equation iteratively to improve the accuracy. The number of Fourier terms is increased automatically. The well-known sunflower equation and van der Pol equation with unit delay are given as numerical examples. Their solutions are verified for a wide range of system parameters. Comparison with those available shows that the residue harmonic balance method is effective to solve the autonomous delay differential equations. Moreover, the present method works not only in determining the amplitude but also the frequency at bifurcation. [Copyright &y& Elsevier]

The wear surfaces abraded with quartzite and granite were subjected to scratch tests. Sharp and blunt indenters were used with various constant loads to produce controlled abrasive wear tracks. The characteristics of deformation mechanisms and material removal were further studied using a scanning electron microscope to determine the differences in the tribological behaviour between the quartzite and granite wear surfaces. The results indicate that quartzite residues are more uniformly distributed as individual particles on the wear surfaces and therefore provide more stable frictional forces. In the case of granite the abrasive residues are rather non-uniformly collected into piles of abrasives. [ABSTRACT FROM AUTHOR]

The study of sum and product problems in finite fields motivates the investigation of additive structures in multiplicative subgroups of such fields. A simple known fact is that any multiplicative subgroup of size at least q in the finite field F must contain an additive relation x + y = z. Our main result is that there are infinitely many examples of sum-free multiplicative subgroups of size Ω( p) in prime fields F. More complicated additive relations are studied as well. One representative result is the fact that the elements of any multiplicative subgroup H of size at least q of F can be arranged in a cyclic permutation so that the sum of any pair of consecutive elements in the permutation belongs to H. The proofs combine combinatorial techniques based on the spectral properties of Cayley sum-graphs with tools from algebraic and analytic number theory. [ABSTRACT FROM AUTHOR]

We determine the Lind Lehmer constant for groups of the form Zpn. [ABSTRACT FROM AUTHOR]

The most natural seminearrings, i.e., the seminearrings of all self-maps of additive semigroups are necessarily multiplicatively regular but they need not be additively regular. The purpose of this paper is to investigate additively regular seminearrings. We mainly focus on the study of congruences in various types of additively regular seminearrings such as additively inverse, additively Clifford and Bandelt seminearrings. We deduce that for a restricted type of additively inverse seminearrings there exists an inclusion preserving bijective correspondence between the set of all normal congruences and that of all full k-ideals. Finally, we characterize those seminearrings which are the subdirect product of a distributive lattice and a zero symmetric near-ring. [ABSTRACT FROM AUTHOR]

We provide unconditional results and conditional ones under the assumption of GRH (Generalized Riemann Hypothesis) on the distribution of quadratic residues and quadratic non-residues in , where is an RSA modulus used in the Goldwasser-Micali cryptosystem. The paper also discusses cryptographic implications of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, a new class of (N,K) near-optimal partial Hadamard codebooks is proposed. The construction of the proposed codebooks from Hadamard matrices is based on binary row selection sequences, which are generated by quadratic residue mapping of p -ary m -sequences. The proposed codebooks have parameters and K=({p-1}/{2p})(N+\sqrt{N})+1 for an odd prime p$ and an even positive integer $n$ . We prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large $p$ and derive their inner product distribution. [ABSTRACT FROM PUBLISHER]

We determine the Lind Lehmer constant for groups of the form Zpn. [ABSTRACT FROM AUTHOR]

In recent years non-woven bag filters have been used in waste incinerators for the efficient collection of dust and removal of detrimental gas. However, dust collection efficiency decreases with time until the bag filters are no longer effective. Dust adhering to the fabric is a major determinant of bag filter life. In the present study a flat filter was used to study the relationship between various parameters of a bag filter structure and its dust dislodgement efficiency. The results confirm that fiber linear density, modulus of elasticity, and the form of the fiber cross-section of the felt can each affect the dust collection efficiency of a bag filter. Higher fiber linear density in a bag filter prevents dust from penetrating the filter, and this allows the dust to be more easily dislodged from the filter. Examination of various forms of fiber cross-section indicates that for the same fiber linear density the triangular form is better than the circular form. A lower Young's modulus allows the fiber to bend more easily and prevents the dust from penetrating the filter. Fiber linear density, fiber modulus of elasticity and form of the fiber cross-section are the variables affecting bag filter efficiency. [ABSTRACT FROM PUBLISHER]

The -residue of a graph, introduced by Jelen in a 1999 paper, is a lower bound on the -independence number for every positive integer . This generalized earlier work by Favaron, Mahéo, and Saclé, by Griggs and Kleitman, and also by Triesch, who all showed that the independence number of a graph is at least as large as its Havel–Hakimi residue, defined by Fajtlowicz. We show here that, for every positive integer , the -residue of disjoint unions is at most the sum of the -residues of the connected components considered separately, and give applications of this lemma. Our main application is an improvement on Jelen’s bound for connected graphs which have a maximum degree cut-vertex. We demonstrate constructively that, in some cases, our extensions give better approximations to the -independence number than all known lower bounds—including bounds of Hopkins and Staton, Caro and Tuza, Favaron, Caro and Hansberg, as well as Jelen’s -residue bound itself. Additionally, we apply this disjoint union lemma to prove a theorem for function graphs (those graphs formed by connecting vertices from a graph and its copy according to a given function) while simultaneously giving, in this context, different classes of non-trivial examples for which our new results improve on the -residue, further motivating our first application of the lemma. [ABSTRACT FROM AUTHOR]

We prove some results concerning the distribution of quadratic residues and nonresidues in arithmetic progressions in the setting $ {{\mathbb{F}}_p}={{\mathbb{Z}} \left/ {{p\mathbb{Z}}} \right.} $, where p is a large prime. [ABSTRACT FROM AUTHOR]

Highlights: [•] Novel technique to reduce search space of an object detector. [•] Multi-scale spectral residue analysis of images to find regions of interest. [•] Evaluation of several contrast normalization techniques to enhance performance. [•] In-depth analysis of impact on detector performance and runtime speed. [ABSTRACT FROM AUTHOR]

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper. [ABSTRACT FROM AUTHOR]

Molecularly imprinted organic–inorganic hybrid composite materials (MIP-HCMs) with controlled swelling and adsorption properties were prepared through copolymerization and the sol–gel process by using doxycycline (DC) as the template molecule, methacrylic acid (MAA) as a functional monomer, methacryloxypropyltrimethoxysilane (KH-570) as a coupling agent and TEOS as an inorganic precursor. By means of changing polymerization conditions as well as the copolymerization ratio of the inorganic precursor and the organic functional monomer, the properties of sorbents can be adjusted for different needs. So the effect of preparation conditions on the structure of the material was studied. The polymer group, thermal stability, adsorption and selectivity characteristics, and the volume swelling degree of the MIP-HCMs were characterized by FTIR, TGA, and dynamic adsorption and swelling experiments, respectively. It was observed that the MIP-HCMs exhibited the highest selectivity (4.9), maximum adsorption capacity (58.2 mg g−1) and good thermal stability. The obtained MIP-HCM was used as an adsorbent for solid-phase extraction of tetracyclines from the milk and honey samples. The average recoveries of three tetracycline antibiotics (DC, tetracycline and chlortetracycline) were obtained in the range of 74.7–115.5% with the precision of 2.1–4.9%. The limits of detection and quantitation of the proposed method were in the range of 4.9–15.3 μg kg−1 and 16.6–51.0 μg kg−1 for the milk samples, and 8.3–15.1 μg kg−1 and 18.3–50.2 μg kg−1 for the honey samples, respectively. [ABSTRACT FROM AUTHOR]

• A new design of an acoustic diffuser based on the construction rules of the Sierpinski triangle is proposed. • The effects of the fractal parameters on the diffusion performance are investigated based on simulations and measurements. • The acoustic diffusion capability is improved by the fractal acoustic diffusers in terms of bandwidth and low-frequency performance compared to the conventional QRD. This paper proposes a new design of an acoustic diffuser based on the construction rules of the Sierpinski triangle in order to broaden the effective diffusion frequency range. The diffuser is made of triangular blocks of different sizes attached to a plane surface. The effects of the number of fractal iterations, the height of triangular blocks, and arrangements of the blocks on the normal-incidence diffusion coefficients in the near field are examined through numerical simulations based on the boundary element method (BEM) in the frequency range of 100 Hz – 5 kHz. Furthermore, measurement results will be presented to validate the diffusion performance presented by the numerical simulations. The diffusion performance of a conventional quadratic residue diffuser (QRD) is compared to confirm the advantage of the designed diffuser for broadening the effective frequency range. It shows that the fractal patterns with various sizes of blocks improve diffusion performance compared to the conventional QRD of the same size, especially in the mid-low frequency range below 1 kHz. [ABSTRACT FROM AUTHOR]

We give a tight bound for the triple intersection numbers of Paley graphs. In particular, we show that any three vertices have a common neighbor in Paley graphs of order larger than 25. [ABSTRACT FROM AUTHOR]

PP., $99.00, ISBN 978-1-4704-4158-6 The I Introduction i is a condensed version of the I Masterclass, i containing just what is needed for a first course in number theory; but if you have even the slightest interest in number theory, I strongly suggest that you go for the I Masterclass, i which in its almost 600 pages contains a wonderful wealth of material. Furthermore, Granville makes very good use of a peculiar characteristic of number theory, the existence of many intriguing open problems, easy to state and devilishly difficult to solve, introducing them from the very beginning (there is an open problem mentioned already in Chapter 1). [Extracted from the article]

Abstract: We explicitly study Katoʼs residue homomorphisms in Milnor K-theory, which are closely related to Contou-Carrère symbols. As applications we establish several reciprocity laws for certain locally defined maps on K-groups that are associated to arithmetic surfaces. [Copyright &y& Elsevier]

In this paper we consider the following two equivalence relations on the lattice 𝒞(S) of all congruences on a semigroupSwith the set of idempotentsES:where kerρ = {x ∈ S: (x,x2) ∈ ρ} and trρ = ρ ∩ (ES × ES) (ρ ∈ 𝒞(S)). We show that ifSis idempotent-surjective, then every κ-class ρκ (ρ ∈ 𝒞(S)) coincides with some interval [ρκ, ρκ]. We study idempotent pure andE-disjunctive congruences on an arbitrary idempotent-surjective semigroup. In particular, we show that if τ is the greatest idempotent pure congruence on an idempotent-surjective semigroupS, thenS/τ isE-disjunctive (see Section 2). In Section 3 we investigate the trace class ρθ (ρ ∈ 𝒞(S)) of an arbitrary idempotent-surjective semigroupS. Also, we study the connections between ρ ∈ 𝒞(S) and four associated (with ρ) congruences ρκ, ρκ, ρθ, ρθ. In particular, using a conjunction between the least Clifford congruence ξ (on an eventually regular semigroup) and the congruences ξκ, ξθ, we give the necessary and sufficient conditions for ξ to be idempotent pure (see Section 4). In Section 5 we describe allE-unitary congruences on an arbitrary idempotent-surjective semigroup. Finally, some remarks concerning stronglyE-reflexive congruences on an eventually regular semigroup are given (see Section 6). [ABSTRACT FROM AUTHOR]

In the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals. [ABSTRACT FROM AUTHOR]

Mouse cytotoxic T-lymphocyte antigen-2α (CTLA-2α), Drosophila CTLA-2-like protein (crammer), and Bombyx cysteine protease inhibitor (BCPI) belong to a novel family of cysteine protease inhibitors (I29). Their inhibitory mechanisms were studied comparatively. CTLA-2α contains a cysteine residue (C75),which is essential for its inhibitory potency. TheCTLA-2α monomerwas converted to a disulfide-bonded dimer in vitro and in vivo. The dimer was fully inhibitory, but the monomer, which possessed a free thiol residue, was not. A disulfide-bonded CTLA-2α/cathepsin L complex was isolated, and a cathepsin L subunit with a molecular weight of 24,000 was identified as the interactive enzyme protein. Crammer also contains a cysteine residue (C72). Both dimeric and monomeric forms of crammer were inhibitory. A crammer mutant with Cys72 to alanine (C72A) was fully inhibitory, while the replacement of Gly73 with alanine (G73A) caused a significant loss in inhibitory potency, which suggests a different inhibition mechanism from CTLA-2α. BCPI does not contain cysteine residue. C-terminal region (L77-R80) of BCPI was essential for its inhibitory potency. CTLA-2α was inhibitory in the acidic pH condition but stabilized cathepsin L under neutral pH conditions. The different inhibition mechanisms and functional considerations of these inhibitors are discussed. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) and metadynamics techniques were used to study the cellulase Cel48F-sugar. Cellulase is enzyme that breaks cellulose fibers into small sugar units and is potentially useful in second generation alcohol production. In MD simulations, the overall structure of equilibrated Cel48F did not significantly change along the trajectory, retaining root mean square deviation below 0.15 nm. A set of 15 residues interacting with the sugar chains via hydrogen bonding throughout the simulation was observed. Thefree energy of dissociation (Δdiss.) of the chains in the catalytic tunnel of Cel48F was determined by metadynamics. TheΔdiss. values of the chains entering and leaving the wild-type Cel48F cavity were 13.9 and 62.1 kcal/mol, respectively. We also mutated the E542 and Q543 to alanine residue and obtained Δdiss. of 41.8 and 45.9 kcal/mol, respectively. These mutations were found to facilitate smooth dissociation of the sugar chain across the Cel48F tunnel. At the entry of the Cel48F tunnel, three residues were mutated to alanine: T110, T213, and L274. Contrary to the T110A-Cel48F, the mutants T213-Cel48F and L274-Cel48F prevented the sugar chain frompassing across the leaving site. Thepresent results can be a guideline inmutagenesis studies to improve processing by Cel48F. [ABSTRACT FROM AUTHOR]

We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work is the recent equidistribution results of N. Katz. [ABSTRACT FROM AUTHOR]

Two-parameter families of straight lines (line congruences) are implicitly present in graphics and geometry processing in several important ways including lighting and shape analysis. In this paper we make them accessible to optimization and geometric computing, by introducing a general discrete version of congruences based on piecewise-linear correspondences between triangle meshes. Our applications of congruences are based on the extraction of a so-called torsion-free support structure, which is a procedure analogous to remeshing a surface along its principal curvature lines. A particular application of such structures are freeform shading and lighting systems for architecture. We combine interactive design of such systems with global optimization in order to satisfy geometric constraints. In this way we explore a new area where architecture can greatly benefit from graphics. [ABSTRACT FROM AUTHOR]

For monogenic (continuous and Gâteaux-differentiable) functions taking values in a three-dimensional harmonic algebra with two-dimensional radical, we compute the logarithmic residue. It is shown that the logarithmic residue depends not only on the roots and singular points of a function but also on the points at which the function takes values in the radical of a harmonic algebra. [ABSTRACT FROM AUTHOR]

Abstract: Spaced seeds are used in approximate pattern matching algorithms to quickly discard regions where a match is not likely to occur. We propose a family of lossless spaced seeds based on Quadratic Residues modulo a prime number. Our seeds work with a threshold in the sense that two regions are considered similar only if the seed hits t times within the regions. We prove that, for any number of errors, our seeds have an exponentially smaller probability of producing false positive matches than any traditional seed using a threshold . To establish our result we introduce a formal notion of selectivity that generalizes the concept of seed weight, and we relate it to the minimum coverage and to a new structural property defined in terms on seed rotations. This groundwork will be useful for further analysis on seeds with threshold and we use it to provide improved bounds for approximate matching with 2 or 3 errors. Our results show that the use of a single seed with a threshold should be considered as a possible alternative to single or multiple seeds with . [Copyright &y& Elsevier]

Highlights: [•] Congruence between biodiversity and ecosystem services is weak at the local scale. [•] Regulating and most cultural services may be spatially congruent with biodiversity. [•] Primary data could maximize the congruence of biodiversity and ecosystem services. [•] Systematic conservation maximizes both ecosystem services and biodiversity. [•] Cost-benefit ratio favors conservation when ecosystem services are considered. [Copyright &y& Elsevier]

Abstract: We show in this study that the presence of trace metal residues in some supposedly metal-free catalysts for oxygen reduction, at concentrations which are difficult to detect using conventional methods such as XPS and EDX, can profoundly promote the ORR activity of the catalysts. [Copyright &y& Elsevier]

Abstract: Interfacial side-reactions at a LiNi0.5Mn1.5O4 spinel electrode in LiPF6/organic carbonate-based electrolyte were investigated using FTIR and fluorescence spectroscopy. In situ measurements at a carbon- and binder-free LiNi0.5Mn1.5O4 electrode showed formation of fluorescent species that coincides with the oxidation of NiII+ in LiNi0.5Mn1.5O4. The majority of these electrolyte oxidation products diffuse away into the electrolyte but fluorescence images of cycled LiNi0.5Mn1.5O4 composite electrodes also show fluorescent residues at the surface of the electrode. FTIR and Raman spectra of the surface layer indicate formation of metal-ion doped organic and inorganic compounds upon electrolyte oxidation at potentials above 4.2V. [Copyright &y& Elsevier]

A celebrated unresolved conjecture of Erdös and Hajnal (see Discrete Appl Math 25 (1989), 37-52) states that for every undirected graph H, there exists [ABSTRACT FROM AUTHOR]

Abstract: It is described how my contacts with a group of functional analysts in Chemnitz (Germany) came along and resulted in a longstanding cooperation on logarithmic residues and spectral regularity in a Banach algebra setting. [Copyright &y& Elsevier]

Let $G$ be a connected, reductive algebraic group over a number field $F$ and let $E$ be an algebraic representation of ${G}_{\infty } $. In this paper we describe the Eisenstein cohomology ${ H}_{\mathrm{Eis} }^{q} (G, E)$ of $G$ below a certain degree ${q}_{ \mathsf{res} } $ in terms of Franke’s filtration of the space of automorphic forms. This entails a description of the map ${H}^{q} ({\mathfrak{m}}_{G} , K, \Pi \otimes E)\rightarrow { H}_{\mathrm{Eis} }^{q} (G, E)$, $q\lt {q}_{ \mathsf{res} } $, for all automorphic representations $\Pi $ of $G( \mathbb{A} )$ appearing in the residual spectrum. Moreover, we show that below an easily computable degree ${q}_{ \mathsf{max} } $, the space of Eisenstein cohomology ${ H}_{\mathrm{Eis} }^{q} (G, E)$ is isomorphic to the cohomology of the space of square-integrable, residual automorphic forms. We discuss some more consequences of our result and apply it, in order to derive a result on the residual Eisenstein cohomology of inner forms of ${\mathrm{GL} }_{n} $ and the split classical groups of type ${B}_{n} $, ${C}_{n} $, ${D}_{n} $. [ABSTRACT FROM AUTHOR]

Abstract: Let be an infinite set of nonempty, finite subsets of the positive integers. If p is an odd prime, let denote the cardinality of the set . When is constructed in various ways from the set of all arithmetic progressions of positive integers, we determine the sharp asymptotic behavior of as . Generalizations and variations of this are also established, and some problems connected with these results that are worthy of further study are discussed. [Copyright &y& Elsevier]

Abstract: Given a commutative Noetherian local ring R, the linearity defect of a finitely generated R-module M, denoted , is an invariant that measures how far M and its syzygies are from having a linear resolution. Motivated by a positive known answer in the graded case, we study the question of whether implies . We give answers in special cases, and we discuss several interpretations and refinements of the question. [Copyright &y& Elsevier]

ABSTRACT Digital signatures are one of the fundamental security primitives because they provide authenticity and nonrepudiation in the broadcast/multicast communication networks. However, the current broadcast/multicast authentication standards are vulnerable to signature flooding because excessive signature verification requests exhaust the computational resource of victims. The situation becomes worse in the case of the energy-constrained networks such as wireless sensor networks and mobile ad hoc networks. As an essential variation of ordinary digital signature schemes, multisignature schemes enable a single compact signature to authenticate a message under a set of different signers. In this paper, we first propose an efficient identity-based multisignature scheme with three interactive rounds under quadratic residue assumption, which equals to the large integer factoring assumption. By using the technique of quadratic residue-based multiplicatively homomorphic equivocable commitment, an advanced identity-based multisignature scheme is proposed to achieve to reduce the interactive round complexity to two rounds. We give the formal security proof that our schemes are existentially unforgeable under adaptively chosen message attacks and chosen identity attacks in the random oracle model. Compared with the previous work, our schemes are very efficient. In particular, our schemes are featured by the weak assumption and the efficient signing and verification procedures. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Let be a prime, and let m be an integer with . In this paper, based on the work of Brillhart and Morton, by using the work of Ishii and Deuringʼs theorem for elliptic curves with complex multiplication we solve some conjectures of Zhi-Wei Sun concerning . [Copyright &y& Elsevier]

Abstract: In this note, by the umbral calculus method, the Sun and Zagier congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also presented. [Copyright &y& Elsevier]

Abstract: Text: We prove two congruence results concerning Kloosterman sums over finite fields. The first result concerns the coefficients of the characteristic polynomial over of a Kloosterman sum, and the second result gives a characterisation of ternary Kloosterman sums modulo 27. We use methods from algebraic number theory such as Stickelbergerʼs theorem and the Gross–Koblitz formula, as well as Fourier analysis. Video: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=VJcB6W_PQ0s. [Copyright &y& Elsevier]

Given an integer N ≥ 3, we shall prove that for all primes p ≥ ( N − 2)4, there exists x in (ℤ/ pℤ) such that x, x + 1, ..., x + N − 1 are all squares (respectively, non-squares) modulo p. Similarly, for an integer N ≥ 2, we prove that for all primes $\displaystyle p \geq \exp(2^{5.54N})$, there exists an element x ∈ (ℤ/ pℤ) such that x, x + 1, ..., x + N − 1 are all generators of (ℤ/ pℤ). [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate 2-parts of class numbers of quadratic imaginary field and 2-parts of the algebraic parts of the central L-values associated to the elliptic curves by studying congruences modulo small powers of two between certain half-integral weight modular forms. Assuming the full Birch and Swinnerton–Dyer conjecture for elliptic curves , we prove results about the structure of the 2-part of the Tate–Shafarevich group . Bruin and Hemenway (2011) [3] unconditionally proved some of these results, therefore we verify that for curves Birch and Swinnerton–Dyer conjecture gives correct predictions about the size of 2-part of its Tate–Shafarevich group. [Copyright &y& Elsevier]

Abstract: Using a p-adic monodromy theorem on the affine ordinary locus in the minimally compactified moduli scheme modulo powers of a prime p of abelian varieties, we extend Katzʼs results on congruence and p-adic properties of elliptic modular forms to Siegel modular forms of higher degree. [Copyright &y& Elsevier]

Abstract: For every integer k, a k-representation of is a string of nonnegative integers such that , and is their number. We present an efficient recursive formula for ; this formula allows also to prove the congruence for . [Copyright &y& Elsevier]

We prove that when $(a, m)= 1$ and $a$ is a quadratic residue $\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$, there are infinitely many Carmichael numbers in the arithmetic progression $a\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$. Indeed the number of them up to $x$ is at least ${x}^{1/ 5} $ when $x$ is large enough (depending on $m$). [ABSTRACT FROM AUTHOR]

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of ℕ is a set of quadratic residues for infinitely many primes of the form [ n] with 1 ≤ c ≤ 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects. [ABSTRACT FROM AUTHOR]

In this paper, Three decoding methods of the (89, 45, 17) binary quadratic residue (QR) code to be presented are hard, soft and linear programming decoding algorithms. Firstly, a new hybrid algebraic decoding algorithm for the (89, 45, 17) QR code is proposed. It uses the Laplace formula to obtain the primary unknown syndromes, as done in Lin et al.'s algorithm when the number of errors v is less than or equal to 5, whereas Gaussian elimination is adopted to compute the unknown syndromes when v ≥ 6. Secondly, an appropriate modification to the algorithm developed by Chase is also given in this paper. Therefore, combining the proposed algebraic decoding algorithm with the modified Chase-II algorithm, called a new soft-decision decoding algorithm, becomes a complete soft decoding of QR codes. Thirdly, in order to further improve the error-correcting performance of the code, linear programming (LP) is utilized to decode the (89, 45, 17) QR code. Simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with Lin et al.'s hard decoding algorithm, and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate (BER) performance. Moreover, the LP-based decoding improves the error-rate performance almost without increasing the decoding complexity, when compared with the new soft-decision decoding algorithm. It provides a coding gain of 0.2 dB at BER = 2 x 10^-6. [ABSTRACT FROM PUBLISHER]

ABSTRACT In EUROCRYPT 2009, Hofheinz and Kiltz introduced a new practical chosen ciphertext secure public-key encryption scheme under the assumption that factoring is intractable. They also proposed a variant that features a slightly more efficient decryption but unfortunately leads to large public key, of size about O( k), where k is a security parameter. In this paper, we propose a novel method to balance the efficiency and the key size of those previous two schemes. Although the public key in our scheme only consists of one RSA modulus and three group elements, it is still more efficient at decrypting than Hofheinz and Kiltz's scheme. By remarking that under certain assumptions factoring the modulus is still hard over much smaller subgroups of signed quadratic residues (i.e., semismooth subgroup), we were able to construct a new scheme that performs extremely efficient decryption. In fact, to date, this is the most efficient scheme for decryption among all public-key encryption schemes (mainly including Hofheinz and Kiltz's schemes and their follow-up works) whose security against chosen ciphertext attacks is based on the intractability of factoring in the standard model. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let $p$ be a prime. In this paper, we present a detailed $p$-adic analysis on factorials and double factorials and their congruences. We give good bounds for the $p$-adic sizes of the coefficients of the divided universal Bernoulli number ${B}_{n} / n$ when $n$ is divisible by $p- 1$. Using these, we then establish the universal Kummer congruences modulo powers of a prime $p$ for the divided universal Bernoulli numbers ${B}_{n} / n$ when $n$ is divisible by $p- 1$. [ABSTRACT FROM AUTHOR]