An addition chain for a positive integer n is a set 1 = a0 < a1 < ... < a(r) = n of integers such that for each i greater-than-or-equal-to 1, a(i) = a(j)+ a(k) for some k less-than-or-equal-to j < i. This ...
An addition chain for a positive integer n is a set 1 = a0 < a1 < ... < a(r) = n of integers such that for each i greater-than-or-equal-to 1, a(i) = a(j)+ a(k) for some k less-than-or-equal-to j < i. This paper introduces the function NMC(n) which denotes the number of minimal addition chains for an integer n. The function is explicitly determined on certain classes of integers, and its relation to factor chains is explored. In particular the concept of a normal integer is introduced, and lower bounds for NMC(n) are developed for normal integers for which the factor chain method produces a minimal addition chain.
be stored or transmitted in an efficient *** this work,a new idea is proposed,where we take advantage of the redundancy that appears in a group of images to be all compressed together,instead of compressing each image...
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be stored or transmitted in an efficient *** this work,a new idea is proposed,where we take advantage of the redundancy that appears in a group of images to be all compressed together,instead of compressing each image by *** our proposed technique,a classification process is applied,where the set of the input images are classified into groups based on existing technique like L1 and L2 norms,color *** images that belong to the same group are compressed based on dividing the images of the same group into sub-images of equal sizes and saving the references into a *** the process of extracting the different sub-images,we used the mean squared error for comparison and three blurring methods(simple,middle and majority blurring)to increase the compression *** show that varying blurring values,as well as MSE thresholds,enhanced the compression results in a group of images compared to JPEG and PNG compressors.
Acetaminophen and caffeine are analgesic or psychoactive drugs in human life that plays a major role in food and medicinal chemistry. Caffeine increases the efficacy of acetaminophen by improving its absorption, there...
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Acetaminophen and caffeine are analgesic or psychoactive drugs in human life that plays a major role in food and medicinal chemistry. Caffeine increases the efficacy of acetaminophen by improving its absorption, thereby prolonging analgesic action. Caffeine might exacerbate symptoms of anxiety if being prone to them. Taking these medications for a headache or migraine may cause problems for human life. Developing a sensitive, selective, easy, quick, and economical electroanalytical approach for the simultaneous detection of acetaminophen and caffeine has been a major area of research since they typically coexist in biological fluids and oxidize at overlapping potentials. Voltammetry has become one of the most commonly used and an important method amongst the other methods due to its high sensitivity and reliability. Moreover, carbon materials, metal/metal oxides/nanoparticles, and polymer-based materials have enhanced researchers' attention for the strategy and growth of electrochemical sensors for acetaminophen and caffeine. This compilation is a comprehensive effort to address the growing need for materials and their simultaneous detection of acetaminophen and caffeine. In this study, the validation parameters (electrode surface area, catalytic activity, electron transfer kinetics, potential window, sensitivity, and selectivity) were evaluated and provided a strong foundation for evaluating the effectiveness of materials and techniques. This review highlights the most widely used voltammetric methods for simultaneous electrochemical determination of acetaminophen and caffeine, and it explains the interference effect of acetaminophen and caffeine along with similar structural components. Finally, the topic has been concluded with existing challenges and prospects.
We show in a uniform setting the crucial role of compactness in the theory of the Smyth powerdomain of streams. The topological notion of compactness is characterized in an order- theoretical manner, involving a notio...
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We show in a uniform setting the crucial role of compactness in the theory of the Smyth powerdomain of streams. The topological notion of compactness is characterized in an order- theoretical manner, involving a notion of bounded sets. We obtain general results on the continuity of operators, and consider applications as diverse as interleaving, hiding and stream programming operators.
The problem is considered of determining, for a rectangular matrixT, the smallest perturbation of a given submatrix that lowers the rank ofT. For different classes of matrix norms, it is shown how the solution of the ...
The problem is considered of determining, for a rectangular matrixT, the smallest perturbation of a given submatrix that lowers the rank ofT. For different classes of matrix norms, it is shown how the solution of the problem can be obtained through an equivalent, often simpler, problem.
The numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered in this Letter. We construct new symplectic and trigonometrically symplectic methods of second and t...
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The numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered in this Letter. We construct new symplectic and trigonometrically symplectic methods of second and third order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis. (c) 2006 Elsevier B.V. All rights reserved.
Let SeH{0}(k) [NSeH{0}(k)] denote the class of languages over a one-letter alphabet accepted by two-way sensing deterministic [nondeterministic] k-head finite automata. This paper shows that (i) SeH{0}(2) not subset o...
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Let SeH{0}(k) [NSeH{0}(k)] denote the class of languages over a one-letter alphabet accepted by two-way sensing deterministic [nondeterministic] k-head finite automata. This paper shows that (i) SeH{0}(2) not subset of or equal to SeH{0}(3), and (ii) NSeH{0}(2)not subset of or equal to NSeH{0}(3). This gives an affirmative answer to an open problem in Ref. [3].
A nonlinear continuous-time Markov chain describing a two-step process of cytolytic cells, binding to target and the subsequent lysis and release of label is shown to have kinetics which resemble standard enzyme-subst...
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A nonlinear continuous-time Markov chain describing a two-step process of cytolytic cells, binding to target and the subsequent lysis and release of label is shown to have kinetics which resemble standard enzyme-substrate kinetics. The Michaelis-Menten saturation function is found as a special case resulting when the target population is in excess. A comparison theorem for the pseudo-steady-state distribution II is constructed to enable examination of that distribution whose expected value E and variance V satisfy -KmE+(CT-E)(TT-E)+V=0, where Km is the Michaelis half-saturation constant and CT and TT are the initial populations of the two cell types. Using II as an initial condition, the release of label process is examined. The main result is that the fraction of specific release, f, has the approximate form .**GRAPHIC**. when TT is large, so that a nonlinear regression procedure is appropriate for the determination of the parameters.
Recently,a family of quadratic APN functions was demonstrated by Bracken et *** exist over F22k with k even and 3 *** family of APN functions was firstly proposed by Budaghyan et *** they exist provided the existence ...
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Recently,a family of quadratic APN functions was demonstrated by Bracken et *** exist over F22k with k even and 3 *** family of APN functions was firstly proposed by Budaghyan et *** they exist provided the existence of a quadratic polynomial of the type x2s+1+cx2s+c2k x+1 with no zeros in *** et *** such polynomials when k is even and 3 *** this paper,we show that such polynomials exist for all even integers *** a result,the APN functions over F22k exist for all even ***,the Walsh spectra of these APN functions is shown to be the same as the one of the Gold APN *** gives a positive answer to one conjecture.
This study aims to address the common issue of biased estimation errors in time series modeling by analyzing the error in locating ideal hyperparameters and defining appropriate validation methods. Specifically, it fo...
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