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The paper presents a new practical method of achieving a dramatic reduction in the size of protocols, to increase transmission rates. The method uses a new code subjected to matrix type-B code, called concatenated quasiquadratic or semiquadratic residue (SQR) matrix code. [ABSTRACT FROM AUTHOR]

Using a free semigroup and a free monoid generated by two symbols, two congruences are introduced. These congruences provide natural equivalence classifications of all finite composite creation and annihilation operators for fermions and bosons such that equivalent operators act identically (to within a nonnegative integer multiple) upon the associated basis states. The resulting quotient structures are shown to be isomorphic to two elementary inverse semigroups and their algebras are used to construct generalized commutation forms. These provide for the easy evaluation of any fermion anticommutator and any reduced word boson commutator. [ABSTRACT FROM AUTHOR]

Reports on a study which explores the role of remaining charged residues by producing and characterizing mutants of anthopleurin B (ApB) at Asp-9, Lys-37, His-39 and His-34. What polypeptide toxins can cause.

Detection of outliers and other diagnostics based on residuals have gained widespread use in linear regression. Logistic regression has been both blessed and hindered by this development. Certainly logistic regression requires procedures to detect global and local model weaknesses. Thus the wealth of work done in linear regression provides guides and suggestions that may, with care and ingenuity, be applied to logistic regression. Several innovative attempts in this direction have been made by authors such as Tsiatis (1980), Pregibon (1979, 1981), Landwehr, Pregibon, and Shoemaker (1984), and Cook and Weisberg (1982). Unfortunately the similarities that allow such techniques to adapt to logistic regression seem, in addition, to hide many of the differences. Two such differences are discussed here. The first examines the effect of events of small probability on estimation in logistic regression. The simple conclusion is that to estimate the probability of success p in an area in which p is small, one must observe events of small probability. This suggests that the motives for outlier detection should be carefully considered. The second difference examined deals with the distribution of residuals. Let Y be the response variable and let x be a p x 1 vector of explanatory variable. In linear regression with normal errors, Y - E(Y | x) is normally distributed with mean 0 and variance sigma[sup 2]. Thus the distribution of this residual from the true model does not depend on the explanatory variables x. This is not true in logistic regression with binary data. There Y has a Bernoulli distribution with probability of success p(x) = Pr(Y = 1 | x). Thus any reasonable definition of a residual from the true model, for example, Y - p(x), has a two-point distribution that depends on x through p(x). That is, each residual... [ABSTRACT FROM AUTHOR]

We assessed the current state of avian molecular systematics by (i) considering some of the historical factors that have shaped the field in the last 20 years (ii) reviewing the most commonly used molecular methods, and (iii) comparing higher-lever phylogenies via congruence analysis. This three-pronged approach permitted us to identify strongly supported aspects of avian phylogeny and to propose technological and methodological explanations when congruence was low. We found, in general, that few areas of higher-level avian phylogeny are well supported and, hence, well understood. One main reason for this is that, despite a great deal of effort, few studies of higher-level avian phylogenetic relationships have been well planned and executed. Some investigations, for example, have bone astray because of preconceptions about rates of molecular evolution and monophyly, and others suffer from such problems as failure to find the shortest tree, lack of an outgroup, use of a nonmetric distance measure, and simple mistakes. This is not to say, however, that available techniques are incapable of reconstructing avian phylogeny. The extent of congruence that we found among branching patterns estimated by different methods, including carefully designed cladistic morphological analyses, indicates that when applied appropriately, a variety of methods provide useful insight into phylogeny. [ABSTRACT FROM AUTHOR]

The article focuses on the study of double weak stone algebras that shows duality in their properties. It mentions that the main objective for this investigation is to show that linked double weak Stone algebras has equationally definable congruences and provides a complete description by Hasse diagrams.

The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable. [ABSTRACT FROM AUTHOR]

Orthogonal cyclic sequences with low multiplicity of values are given for application to spread spectrum communications systems. Two-, three-, and five-valued orthogonal cyclic sequences are obtained by representing real orthogonal cyclic sequences of length N by cosine series possessing phase constant of odd function, or even function with values (0, π), and by relating the phase constant to quadratic residues of N. We use the fact that an extended quadratic Residue sequence taking values (0, +1, -1) Becomes a sequence of odd function satisfying homogeneous equation of discrete sine transform when N is a prime number of the form N = 4l - 1 (l is a natural number). When N is a prime number of the form N = 4l + 1, the sequence becomes that of even function satisfying a homogeneous equation of discrete cosine transform. Three-valued orthogonal cyclic sequences are obtained by adding a dc component to quadratic residue sequences of these odd and even functions. A two-valued orthogonal cyclic sequence is obtained when a phase constant is given by a quadratic residue sequence of odd function multiplied by a constant. Moreover, when the phase constant is a monomial of odd power and is related to the quadratic residue sequence, a three-valued orthogonal cyclic sequence is obtained for the prime N = 4l - 1. Since N sequences obtained by shifting one of those sequences form an orthogonal system, cross-talk does not occur when these sequences are applied to synchronous spread spectrum multiple access. [ABSTRACT FROM AUTHOR]

Presents a binary quadratic residue number system (QRNS) with noncoprime moduli. Theory for constructing multimoduli QRNS systems; Mathematical basis for constructing multimoduli QRNS systems with noncoprime moduli of forms 2n+1; Comparison of the various QRNS systems; Multimoduli systems with noncoprime moduli.

The article focuses on the study of iterated residues as well as multiple Bernoulli polynomials (MBP), which have rational coefficients. It mentions that the MBPs are natural generalizations of the classical Bernoulli polynomials which correspond to the one-dimensional case. It also mentions the topology of the moduli spaces and the Verlinde-type deformation.

Presents information on the development of the time-frequency hop codes which was based upon extended quadratic congruences (TFHC-EQC). Defintion of a time-frequency hop code; Significant description of time-frequency hop codeword; Information on a lemma which asserts that time-frequency hop codes have good periodic ambiguity functions.

Combining parallel multiple recursive sequences provides an efficient way of implementing random number generators with long periods and good structural properties. Such generators are statistically more robust than simple linear congruential generators that fit into a computer word. We made extensive computer searches for good parameter sets, with respect to the spectral test, for combined multiple recursive generators of different sizes. We also compare different implementations and give a specific code in C that is faster than previous implementations of similar generators. [ABSTRACT FROM AUTHOR]

Explores estimation method and correlations between disturbances of different structural equations and residual path coefficients in both recursive and nonrecursive causal models. Differences between the two causal models; Preference towards nonrecursive structures; Related problems in the estimation and interpretation of residual path coefficients.

For a system of differentiable convex inequalities, a new bound is given for the absolute error in an infeasible point in terms of the absolute residual. By using this bound a condition number is defined for the system of inequalities which gives a bound for the relative error in an infeasible point in terms of the relative residual. [ABSTRACT FROM AUTHOR]

Copyright of Reading Research Quarterly is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article presents a study on the pesticides residues and other impurities derived from the tank rinsates and exterior washes from spray aircraft operated in California. It says that the study also assessed the rinsing process of the tank. It states that the results shows that rinsing of tanks several times with water disposes residual tank mix. It mentions that residue found in exterior washwaters could only be discharged based on the toxicity and environmental persistence of the pesticides.

Several studies have examined the influence of organizational context (e.g., organization size, environment, strategy) on information systems (IS) performance/success. But very few studies have examined IS structure, and those studies have focused on a particular element of IS structure (e.g., decentralization). Thus, the multidimensional structural configuration of IS as an organizational subunit has escaped research attention. Further, the nature of the task to be performed by the IS subunit as a contextual factor has been virtually ignored in the IS research literature. In this paper, we first develop a congruence model for the task-structure relationship in an information systems development (ISD) subunit setting. Then we test this model as a multivariate relationship followed by subordinate bivariate analyses. Analysis of data from 41 hospitals' ISD subunits reveals that a congruence relationship between task context and the structure of an ISD subunit is present. Our findings also show that an exclusive association exists between uncertainty in the task environment and the decision-making structure. Likewise, the association between equivocality of task content and the control structure of the ISD subunit is also exclusive. Implications of these findings for decision makers and researchers are discussed. [ABSTRACT FROM AUTHOR]

Let D be a positive integer with square-free. For any prime p, the square of p does not divide D. In this paper, using the elementary method and the properties of quadratic non-residues, the upper bound for positive integer solutions (x,y) of the equation x²--D=y! is discussed. It is proved that all the positive integer solutions (x,y) of the equation satisfy y<4 √DlogD. [ABSTRACT FROM AUTHOR]

In a recent study, Li et al. proposed an algorithm for the decoding of binary quadratic residue codes with tiny memory requirements. In this Letter, this algorithm is modified in order to dramatically improve the decoding speed. The case of the (89, 45, 17) binary quadratic residue code is used to illustrate the new algorithm. [ABSTRACT FROM AUTHOR]

The main approaches currently used to construct identity-based encryption (IBE) schemes are based on bilinear mappings, quadratic residues and lattices. Among them, the most attractive approach is the one based on quadratic residues, due to the fact that the underlying security assumption is a well-understood hard problem. The first such IBE scheme was constructed by Cocks, and some of its deficiencies were addressed in subsequent works. In this paper, we focus on two constructions that address the anonymity problem inherent in Cocks' scheme, and we tackle some of their incomplete theoretical claims. More precisely, we rigorously study Clear et al.'s and Zhao et al.'s schemes and give accurate probabilities of successful decryption and identity detection in the non-anonymized version of the schemes. Furthermore, in the case of Zhao et al.'s scheme, we give a proper description of the underlying security assumptions. [ABSTRACT FROM AUTHOR]

In order to compare administered drug dosage patterns between different persons or at different times in the same person, a novel formula is proposed that takes into consideration the application times of a specific drug. The herein presented formula permits the calculation of persisting or residual drug activity as related to a time of reference. The obtained value is based on easily available data such as the absolute amount of particularly given drug doses, the patient's body weight and the time frame in which the drug doses were administered. The only genuine pharmacokinetic parameter that has to be considered is the elimination half-life, which is usually available for most drugs from their basic information. The finally resulting figure is called "residual drug activity coefficient" (RDAC), which is a dimensionless unit and specific for each drug. For its rational use further clinical investigations aiming to correlate the spectrum of possible RDAC levels with corresponding clinical effects represent the next step in the use of this mathematical model. [ABSTRACT FROM AUTHOR]

Abstract: Benign familial neonatal convulsions (BFNC) is a rare, clinically and genetically heterogenous epileptic disorder. Two voltage gated potassium genes, KCNQ2 and KCNQ3, have been identified as genes responsible for BFNC1 and BFNC2 respectively. While as many as 73 mutations of KCNQ2 have been described up to date, only 4 mutations in KCNQ3, 3 of them appearing in exon 5, have been identified. Mutation in exon 6 was found for the first time in a Chinese family, and here we report the same missense mutation of KCNQ3 within exon 6 in a Caucasian family, whose history and clinical picture were in accordance with BFNC. [Copyright &y& Elsevier]

We prove that for every lattice effect algebra, the system of all congruences generated by the prime ideals of the compatibility center separates the elements. This is a common generalization of Chang's representation theorem from 1959 and a result of Graves and Selesnick (Colloq Math 27:21-30, ). [ABSTRACT FROM AUTHOR]

The article offers information the power sum identity and its significance determining the binomial coefficient congruences. It mentions that the effectiveness of the power sum in finding and obtaining the mentioned congruences by Bernoulli and Stirling number theorems as well as the exponential Diophantine equations. Furthermore, the power sum was already proven by Blaise Pascal.

The article presents information about a research on radiation copolymerization of cracking residue. It mentions that this experiment involved the radiation copolymerization of cracking residue with acrylic acid under the affect of radiation as ion exchangers and the products obtained were examined. It further presents the detailed information about the entire process of the experiment.

A novel decoding scheme, called syndrome-weight determination, was proposed by Chang et al. in 2008 for the Golay code, or the (23, 12, 7) quadratic residue code. This method is not only very simple in principle but also suitable for parallel hardware design. Presented is a modified version for any binary quadratic residue codes which has been developed. Because of its regular property, the proposed decoder is suitable for both software design and hardware development. [ABSTRACT FROM AUTHOR]

The calculus of residues is one of the many beautiful tools that comes out of the field of complex variables. The calculus of residues is applied, together with the inversion formula for characteristic functions, to compute the non-gamma probability density function for the sum of gamma variates with different shape parameters. The distribution of the sum of gamma variates is needed in problems in statistical inference, as well as stochastic processes. This derivation seems more elegant than previous methods for deriving the density function of such a sum. Furthermore, the numerical computation is straightforward, especially in any symbolic computer language. [ABSTRACT FROM AUTHOR]

The algebraic decoding of binary quadratic residue codes can be performed using the Peterson or the Berlekamp-Massey algorithm once certain unknown syndromes are determined or eliminated. The technique of determining unknown syndromes is applied to the nonbinary case to decode the expurgated ternary quadratic residue code of length 23. [ABSTRACT FROM AUTHOR]

A novel, fast decoder for the binary quadratic residue code of length 23, or equivalently the famous Golay code is proposed. The core is a new idea to determine the syndrome weight. The decoding algorithm can be implemented with a parallel design, and the decoder based on this algorithm is not only very efficient but also of low area cost. It promises a binary Golay decoder which is faster than available decoders. [ABSTRACT FROM AUTHOR]

The article presents a mathematical problem. It states that a girl going to a well with two jugs, one holding three pints and the other five and she is to come back with precisely four pints of water. The problem is to identify whether this is possible and to search the most efficient way to do it. It is said that the solution to the problem are Euclidean Algorithm, some applications of least residues and minimizing the number of stages through calculating the amount water and select the option with fewer stages.

Let q be a prime, P ⩾ 1 and let N q (P) denote the number of rational primes p ⩽ P that split in the imaginary quadratic field Q (− q). The first part of this paper establishes various unconditional and conditional (under existence of a Siegel zero) lower bounds for N q (P) in the range q 1 / 4 + ε ⩽ P ⩽ q , for any fixed ε > 0. This improves upon what is implied by work of Pollack and Benli–Pollack. The second part of this paper is dedicated to proving an estimate for a bilinear form involving Weyl sums for modular square roots (equivalently Salié sums). Our estimate has a power saving in the so-called Pólya–Vinogradov range, and our methods involve studying an additive energy coming from quadratic residues in F q. This bilinear form is inspired by the recent automorphic motivation: the second moment for twisted L -functions attached to Kohnen newforms has recently been computed by the first and fourth authors. So the third part of this paper links the above two directions together and outlines the arithmetic applications of this bilinear form. These include the equidistribution of quadratic roots of primes, products of primes, and relaxations of a conjecture of Erdős–Odlyzko–Sárközy. [ABSTRACT FROM AUTHOR]

Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper presents a fast algebraic scheme for decoding the binary (41, 21, 9) QR code for correcting up to 4 errors on an one-case-by-one-case basis, in which the calculation of unknown syndromes is eliminated and the conditions for checking for the various numbers of errors that exist in the received word are also simplified compared to those from Lin T. C. et al.'s algorithm, which is a traditional algebraic decoding algorithm (ADA). The computational complexity of the decoder performing the binary (41, 21, 9) QR code is analyzed thoroughly, which demonstrates that the proposed decoding scheme is faster, simpler, and more suitable for implementation than Lin T. C. et al.'s algorithm. Numerical emulation results demonstrate that the proposed decoding scheme achieves the same error-rate performance as Lin T. C. et al.'s algorithm, but it has a significantly decreased the complexity of this decoder in terms of the CPU time. [ABSTRACT FROM AUTHOR]

With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today's world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we give some interesting identities and asymptotic formulas for one kind of counting function, by studying the computational problems involving the symmetry sums of one kind quadratic residues and quadratic non-residues mod   p . The main methods we used are the properties of the Legendre's symbol mod   p , and the estimate for character sums. As application, we solve two open problems proposed by Zhiwei Sun. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that every special congruence subgroup SSp( V, I) of the symplectic group Sp( V ( R)), where R is a ring of stable rank 1 with invertible element 2 and dim V ( R) ≥ 4, is generated by the symplectic transvections belonging to this subgroup. This result is used to obtain the complete description of the normal subgroups of Sp( V ( R)). [ABSTRACT FROM AUTHOR]

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono [7, Problem 7.30]. As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strongest and most general results. For example, for p = 2, a result stronger than Theorem 2 is proved in [2], and a result on some modular curves of genus zero can be found in [8]. It should be easy to apply our method, because of its local nature, to modular curves of arbitrary level, as well as to Shimura curves. [ABSTRACT FROM AUTHOR]

Presents the standard elementary proof of the quadratic reciprocity law. Quadratic residue; Legendre symbol; Chinese remainder theorem; Permutation.

Preparation is one method of increasing the efficiency of crude oil feedstock refining processes. In this stage, the feedstock can be activated by regulating the balance of intermolecular interaction forces within a crude oil disperse system by different methods: external fields (electric, magnetic); mechanical; using different kinds of additives, primarily those with surface–active properties. [ABSTRACT FROM AUTHOR]

Provides information on a study which investigated the weight structure and error-correcting performance of the ternary quadratic-residue code. Description of the error-correcting performance of the quadratic-residue code; Presentation of the algebraic decoding algorithm; Conclusion.

Focuses on determining which numbers between 0 and p/2 are quadratic residues modulo. Computing and plotting the points for twenty values of p; Information on a theorem; Calculation of quadratic residues.

Let p > 3 be a fixed prime. For a supersingular elliptic curve E over F p , a result of Ibukiyama tells us that End (E) is a maximal order O (q) (resp. O ′ (q)) in End (E) ⊗ Q indexed by a (non-unique) prime q satisfying q ≡ 3 mod 8 and the quadratic residue (p q) = − 1 if 1 + π 2 ∉ End (E) (resp. 1 + π 2 ∈ End (E)), where π = ((x , y) ↦ (x p , y p) is the absolute Frobenius. Let q j denote the minimal q for E whose j -invariant j (E) = j and M (p) denote the maximum of q j for all supersingular j ∈ F p. Firstly, we determine the neighborhood of the vertex [ E ] with j ∉ { 0 , 1728 } in the supersingular ℓ -isogeny graph if 1 + π 2 ∉ End (E) and p > q j ℓ 2 or 1 + π 2 ∈ End (E) and p > 4 q j ℓ 2 : there are either ℓ − 1 or ℓ + 1 neighbors of [ E ] , each of which connects to [ E ] by one edge and at most two of which are defined over F p. We also give examples to illustrate that our bounds are tight. Next, under GRH, we obtain explicit upper and lower bounds for M (p) , which were not studied in the literature as far as we know. To make the bounds useful, we estimate the number of supersingular elliptic curves with q j < c p for c = 4 or 1 2. In the appendix, we compute M (p) for all p < 2000 numerically. Our data show that M (p) > p except p = 11 or 23 and M (p) < p log 2 ⁡ p for all p. [ABSTRACT FROM AUTHOR]

In 1991, Shalaby conjectured that any additive group Z n , where n ≡ 1 or 3 (mod 8) and n ≥ 11 , admits a strong Skolem starter and constructed these starters of all admissible orders 11 ≤ n ≤ 57. Only finitely many strong Skolem starters have been known. Recently, in Ogandzhanyants et al. (2019) was given infinite families of them. In this note, an infinite family of strong Skolem starters for Z n , where n ≡ 3 (mod 8) is a prime integer, is presented. [ABSTRACT FROM AUTHOR]