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In this work, an elliptic curve matrix (ECM) is defined over a group ring (GR). This matrix, namely ECMGR is used to design the alternative versions of elliptic curve Diffie-Hellman key exchange (ECDHKE) and elliptic El-Gamal public key cryptosystem (EEPKC). The security of the proposed cryptosystems ECDHKE-ECMGR and EEPKC-ECMGR depended on the hardmathematical problem which is ECMGR-DLP that is also defined as a new concept in this work. New computational results of these proposed cryptosystems are discussed as the study cases with small values of the parameters. The proposed cryptosystems consider as more suitable for communications with more level of the security. [ABSTRACT FROM AUTHOR]

The purposes of this study are to determine and to describe the mathematical problem solving ability of class X students on exponential and logarithmic matters. The type of research used in this study is descriptive qualitative. This study was carried out at one of the South Tangerang City Senior High Schools in the 2021/2022 academic year with the subjects being 40 students of class X MIPA 4. The instruments used to collect data in this study were through observation, test, and interviews. The measurement of mathematical problem solving ability in this study is using the Polya problem-solving stage model. The results of this study indicate that students with low mathematical problem solving abilities have not been able to understand the problem nor the information that is known from the questions given. Students with high and moderate mathematical problem solving abilities are able to understand problems and information that are known from the questions, but are still not good at planning problem solving strategies, implementing strategies, and re-examining the final results of problem solving. The difficulty factors in understanding the problems that were found to be intersect from the three categories are the students' lack of understanding of the concepts and properties of exponentials and logarithms. [ABSTRACT FROM AUTHOR]

The article studied the possibility of dividing by zero on the set of so-called aggregate numbers, as well as the possibility of calculating logarithms and exponential expressions with a negative basis, logarithms with sublogarithmic expressions less than zero. So we can enrich mathematics by the numbers that are obtained when dividing by zero. You can work with aggregate numbers like ordinary fractions, applying the same laws to them. The article describes the need to abandon counting sticks to denote mathematical operations and the use of universal letter symbols to expand the boundaries of mathematical consciousness and further expand mathematical operations. Knowing the source code written in letter mathoperations, you can «reverse», flip the code and get the source data, which is important for computer science. This way you can save all the operations performed with the number. [ABSTRACT FROM AUTHOR]

A collection (A1,..., Ak) of subsets of a group G is called k-solution-free if the equation x1 + + xk = 0 has no solution in (A1,..., Ak), where x1 ϵ A1,..., xk ϵ Ak. The asymptotic behavior for the logarithm of the number of k-solution-free collections in Abelian groups is obtained. [ABSTRACT FROM AUTHOR]

In this work, the fuzzy mask of the discrete logarithm (DL) encryption schemes has been proposed. These schemes are the Diffie-Hellman key exchange and the El-Gamal public key cryptosystem. The fuzzy mask for these schemes is computed using the triangular fuzzy membership (TFM) function. The purpose of this mask is to increase the security level of the DL encryption schemes with the moderate values of the parameters in compare with the security of the original DL encryption schemes that are need the huge values of the parameters. Some new small experimental results are discussed. The fuzzy masking on the DL encryption schemes considers as a new insight for more secure communications. [ABSTRACT FROM AUTHOR]

We establish large deviation inequalities with exponential decay for the maximum of partial sums of subgaussian random variables. Applying our result to acceptable sequences of bounded mean zero random variables, we strengthen a well-known inequality of Hoeffding. As a consequence we prove a bounded law of iterated logarithm for this class of random variables. The obtained method, also allows us to state a strong integrability property for weighted series of negatively dependent random variables. [ABSTRACT FROM AUTHOR]

Here we suppose that the observed random variable has cumulative distribution function F with regularly varying tail, i.e., 1 − F ∈ RV−α, α > 0. Using the results about exponential order statistics we investigate logarithms of ratios of two order statistics of a sample of independent observations of a Pareto distributed random variable with parameter α. Short explicit formulae for its mean and variance are obtained. Then we transform this function in a proper way to obtain unbiased, asymptotically efficient, and asymptotically normal estimator for α. Finally we simulate Pareto samples and show that in the considered cases the proposed estimator outperforms the well known Hill, t-Hill, Pickands and Deckers-Einmahl-de Haan estimators. [ABSTRACT FROM AUTHOR]

A cryptosystem is a cryptographic scheme that allows a sender to encrypt and send a confidential message or document by using public key, while the receiver can decrypt the encrypted message into its original form by using secret key. Most of the existing cryptosystems are constructed based on single hard number theoretical problems. Furthermore, the concept of group-oriented cryptosystem, known as threshold cryptosystem gives an important role in developing a cryptosystem. In this research, a threshold cryptosystem based on two hard number theoretical problems is presented. The strength of this new threshold cryptosystem is the difficulty to solve both factoring and discrete logarithm problems simultaneously. The security analysis of the scheme shows that it is secure against common security attacks. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating the Pareto front for the optimization of two C² functions. An algorithm is described that is efficient in the sense that the number of function evaluations that are not on the Pareto front grows as the square of the logarithm of the number of function evaluations. [ABSTRACT FROM AUTHOR]

In the paper the calibration technique of the real stress - logarithmic strains uniaxial curves is proposed, based on the modified Bai-Wierzbicki proposition. The material softening was included before the final failure. Four shapes of specimens were tested, to cover a wide range of stress triaxiality conditions and Lode factors. Tests were performed at temperature +20°C, on S355JR steel with ferrlitic- pearlitic microstructure. [ABSTRACT FROM AUTHOR]

Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models. [ABSTRACT FROM AUTHOR]

The logarithm of the estimated next-day wealth return is approximated by k terms of its Taylor series. The resulting Type k universal portfolio generated by the f-divergence is obtained. An implicit form of the portfolio is also obtained by exploiting the mean-value theorem. An empirical study of the performance of the portfolio is focused on the Type 2 Helmbold universal portfolio. A few generalizations of the Helmbold universal portfolio have recently been studied, namely the reverse Helmbold and the parametric Helmbold portfolios. This new type of portfolio can be regarded a contribution to the inventory of Helmbold related universal portfolios. It is verified experimentally that an investor's wealth can be significantly increased by using the Type 2 Helmbold portfolio in investment. [ABSTRACT FROM AUTHOR]

Computation of the tight upper bound on the sample variance of an interval-valued dataset is known to be NP-hard. However, using Ferson's algorithm, the computation of the maximal possible variance over interval-valued dataset can be realized in polynomial time in the maximal number of narrowed intervals intersecting at one point; narrowed means that the intervals are shrinked proportionally to the size of the dataset. Simulation experiments allowed to conjecturing that the maximal number of narrowed intervals intersecting at one point is at most of logarithmic size for a reasonable choice of the data-generating process. Here, we assume uniform distribution of centers and constant radii. Under this setting, we sketch an approach how to prove the polynomiality of computation of upper bound of sample variance over random data. [ABSTRACT FROM AUTHOR]

The golden section sequence of points was defined, and we found that the logarithmic spiral, golden section sequence, and Fibonacci sequence exhibit a close relationship. We considered infinite sums derived from the reciprocals of the golden section numbers and Fibonacci numbers, and infinite sums derived from the reciprocals of the square of the golden section numbers and Fibonacci numbers. Applying the floor function to the reciprocals of these sums, we determined that they are equal to each other. [ABSTRACT FROM AUTHOR]

In 2015, Meshram proposed an efficient ID-based cryptographic encryption based on the difficulty of solving discrete logarithm and integer-factoring problems. The scheme was pairing free and claimed to be secure against adaptive chosen plaintext attacks (CPA). Later, Tan et al. proved that the scheme was insecure by presenting a method to recover the secret master key and to obtain prime factorization of modulo n. In this paper, we propose a new pairing-free ID-based encryption scheme with revocation based on Meshram's ID-based encryption scheme, which is also secure against Tan et al.'s attacks. [ABSTRACT FROM AUTHOR]

Peculiar properties of the BFKL approach in the next-to-next-to-leading logarithmic approximation (NNLLA) are discussed. In this approximation the scheme of derivation of the BFKL equation must be changed because of violation of the simple factorized form of amplitudes with multi-Reggeon exchanges and necessity to take into account imaginary parts of amplitudes in the unitarity relations. [ABSTRACT FROM AUTHOR]

The aim of the present work is to establish explicit conditions for global asymptotic stability of neutral linear fractional differential system with distributed delays. The derivatives in the system can be of Riemann-Liouville or Caputo type. We consider basically the incommensurate case but some results are given for the commensurate case too. The proposed conditions are based on the logarithmic norm technique and part of the results are new even in the particular case of system with constant delays. [ABSTRACT FROM AUTHOR]

Active-thermography has become a well-established Nondestructive Testing (NDT) method for detection of subsurface flaws. In its simplest form, flaw detection is based on visual identification of contrast between a flaw and local intact regions in an IR image sequence of the surface temperature as the sample responds to thermal stimulation. However, additional information and insight can be obtained from the sequence, even in the absence of a flaw, through analysis of the logarithmic derivatives of individual pixel time histories using the Thermographic Signal Reconstruction (TSR) method. For example, the response of a flaw-free multilayer sample to thermal stimulation can be viewed as a simple transition between the responses of infinitely thick samples of the individual constituent layers over the lifetime of the thermal diffusion process. The transition is represented compactly and uniquely by the logarithmic derivatives, based on the ratio of thermal effusivities of the layers. A spectrum of derivative responses relative to thermal effusivity ratios allows prediction of the time scale and detectability of the interface, and measurement of the thermophysical properties of one layer if the properties of the other are known. A similar transition between steady diffusion states occurs for flat bottom holes, based on the hole aspect ratio. [ABSTRACT FROM AUTHOR]

We give a short introduction to the calculation of the leading chiral logarithms, and present the results of the recent evaluation of the LLog series for the nucleon mass within the heavy baryon theory. The presented results are the first example of LLog calculation in the nucleon ChPT. We also discuss some regularities observed in the leading logarithmical series for nucleon mass. [ABSTRACT FROM AUTHOR]

We briefly summarize experimental and theoretical results on the rare decay π0 → e+e-. Two-loop QED corrections are reviewed and the bremsstrahlung contribution beyond the soft-photon approximation is analytically calculated. Using the leading logarithm approximation, the possible contribution of QCD corrections is estimated. The complete result can be used to fit the value of the contact interaction coupling Xr to the recent KTeV experiment with the result X(r)(Mρ) = 4.5 ± 1.0. [ABSTRACT FROM AUTHOR]

This talk includes a short introduction to Chiral Perturbation Theory in the meson sector concentrating on a number of recent developments. I discuss the latest fit of the low-energy constants. Finite volume corrections are discussed for the case with twisted boundary conditions for form-factors and first results at two-loops for three flavours for masses. The last part discusses the extension to other symmetry breaking patterns relevant for technicolour and related theories as well as the calculation of leading logarithms to high loop orders. [ABSTRACT FROM AUTHOR]

LESs are carried out in turbulent channel flows to investigate on the effects of irregular rough surfaces on the mean velocity profiles. In rough walls, due to increase of resistance induced by the wall irregularities, the mean velocity is reduced despite the same pressure gradient drives the current. In literature the downward shift of the streamwise mean velocity profile, in the logarithmic region, is called Roughness Function ΔU+. This shift has been deeply investigated and related to several geometrical parameters, both for regular and irregular roughness geometries. In the fully rough regime it was observed that the roughness function is related to the equivalent sand grain ks through a logarithmic law. Following this theory here a novel logarithmic approach is proposed to determine the roughness function. The results showed that, among the geometrical parameters that characterise the wall geometries, the Effective Slope (ES), which take into account both the height and the texture of the roughness elements, correlates well with the roughness function ΔU+. [ABSTRACT FROM AUTHOR]

We give a short introduction to the calculation of the leading chiral logarithms, and present the results of the recent evaluation of the LLog series for the nucleon mass within the heavy baryon theory. The presented results are the first example of LLog calculation in the nucleon ChPT. We also discuss some regularities observed in the leading logarithmical series for nucleon mass. [ABSTRACT FROM AUTHOR]

The efficiency assessment of acoustic quality monitoring application for research of damages, in particular, the cracks arising at long operation of the heat power equipment is resulted in the present work. The differential equations were first derived describing the change in time delay of surface acoustic waves in the vicinity of the crack, which are directly depending on: a) the argument; b) the plane of states in an implicit form from the parameter of model; c) on a plane of conditions for logarithmic characteristics. [ABSTRACT FROM AUTHOR]

Elliptic Curve Cryptography (ECC) is a public key cryptosystem with a security level determined by discrete logarithm problem called Elliptic Curve Discrete Logarithm Problem (ECDLP). John M. Pollard proposed an algorithm for discrete logarithm problem based on Monte Carlo method and known as Pollard Rho algorithm. The best current bruteforce attack for ECC is Pollard Rho algorithm. In this research we implement modified Pollard Rho algorithm on ECC over GF (241). As the result, the runtime of Pollard Rho algorithm increases exponentially with the increase of the ECC key length. This work also presents the estimated runtime of Pollard Rho attack on ECC over longer bits. [ABSTRACT FROM AUTHOR]

This study aims to investigate the implied adjusted volatility functions using the different Leland option pricing models and to assess whether the use of the specified implied adjusted volatility function can lead to an improvement in option valuation accuracy. The implied adjusted volatility is investigated in the context of Standard and Poor/Australian Stock Exchange (S&P/ASX) 200 index options over the course of 2001-2010, which covers the global financial crisis in the mid-2007 until the end of 2008. Both in- and out-of-sample resulted in approximately similar pricing error along the different Leland models. Results indicate that symmetric and asymmetric models of both moneyness ratio and logarithmic transformation of moneyness provide the overall best result in both during and postcrisis periods. We find that in the different period of interval (pre-, during and post-crisis) is subject to a different implied adjusted volatility function which best explains the index options. Hence, it is tremendously important to identify the intervals beforehand in investigating the implied adjusted volatility function. [ABSTRACT FROM AUTHOR]

Logarithmic HDMR is an HDMR based method and it allows us to reconstruct an analytical structure for a given multivariate analytical function in terms of less variate components. In this study, we develop a method to model multivariate data through Logarithmic HDMR and we use this method to make an approximation to the given original image. That is, we deal with the reconstruction of an image by using Logarithmic HDMR philosophy and we reach very promising results. [ABSTRACT FROM AUTHOR]

In various applications there appear integral equations of the first kind with a kernel which has a logarithmic singularity. The corresponding classes of well-posedness for such equations are Sobolev spaces. We prove the differentiation formulas for weighted singular integrals, which appear in such study, with the goal of its further application to integral equations. [ABSTRACT FROM AUTHOR]

We study the evolution of the von Neumann entropy in a fermionic interacting system at infinite temperature finding two different regimes. A metallic one at low values of the disorder and an insulating regime for strong disorder. In the insulating regime, the entropy evolves logarithmically with time, which is consistent with a Many-Body localized phase, and the slope characterizing this behavior is proportional to the localization length. Finally we have estimated the position of the Many-Body localization transition extrapolating the inverse of this slope in the insulating regime. [ABSTRACT FROM AUTHOR]

Three subjects are examined in connection with the relaxation of an electron glass. 1. In most cases the experimental decay time ris found to relate to a history of the system rather than to the time it takes to reach equilibrium. The reason is that in a non-ergodic system equilibrium cannot be reached in any experiment but the knowledge of an equilibrium property is essential in evaluating the time to reach it. 2. An alternative theory is proposed for the interpretation of aging experiments. The proposed theory is deemed to better represent the physics and is more in keeping with the relaxation theory. 3. A current relaxation theory for the electron glass fails to take into account a certain renewal process during the evolution of the relaxation, namely the possibility of fast transitions following a slow transition. Ramifications of such a neglect are explored. [ABSTRACT FROM AUTHOR]

Bacterial chemoreceptors form two-dimensional sensory arrays on the cell membrane. These sensory arrays, which contain thousands of molecules, detect chemical changes in the environment of the bacterial cell and accordingly control its swimming behaviour, allowing these bacteria to track chemical gradients. It was recently demonstrated that stimulus, by ligand binding, alters the physical organization of these arrays, with dynamics that follow an apparent logarithmic time dependence. Such non-exponential dynamics is often observed in glass-like systems in which the internal dynamics slow down exponentially as the system approaches its equilibrium state. In a few of these 'glassy' systems it was also demonstrated that after altering the equilibrium state of the system for a certain time tw the ensuing relaxation scales with tw. Here, we examined the relaxation of the receptor arrays in the bacterium E. coli after a perturbation by ligand binding for varying periods of times. We find that changing the time tw, during which the stimulus was present, affects mostly the deviation of the receptor arrays from equilibrium, but the dynamics of the relaxation seem to be independent of tw. A possible interpretation is discussed. [ABSTRACT FROM AUTHOR]

Collinear and kT - factorizations were introduced from different theoretical considerations and for different perturbative methods. We demonstrate that they both can be obtained from a more general factorization. We prove that they can be related to each other with imposing a simple assumption for the unintegrated parton distributions [ABSTRACT FROM AUTHOR]

Recently, the development of cryptosystem based on two problems has increased, since it is proved that the cryptosystem based on two problems is more secure than the cryptosystem based on single problem. Meanwhile, the concept of group-oriented cryptography, known as threshold cryptography, gave a new dimension in development of cryptosystems. In this paper we propose a new threshold cryptosystem based on two number theoretical problems; factoring and discrete logarithms. Other than the scheme, we also show that our cryptosystem is secure against some possible attack and requires reasonable time in encryption and decryption phases. [ABSTRACT FROM AUTHOR]

In proxy signature schemes with revocation, an original signer delegates his signing capability to a proxy signer on behalf of the original signer and revokes delegations whenever necessary. Currently, the security of the previous schemes is based on a single hard problem such as factoring or discrete logarithms. These schemes appear secure today but in a near future, if an adversary finds a solution to these hard problems, the developed schemes will be no longer secure. To solve this problem we develop a new proxy signature scheme with revocation based on two hard problems; factoring and discrete logarithms. The new scheme offers higher level security than normal schemes since it is hard for an adversary to solve the two hard problems simultaneously. [ABSTRACT FROM AUTHOR]

This paper presents a new directed signature scheme based on hybrid problems; factoring and discrete logarithm. The scheme allows only an intended verifier to verify the produced signature and provides a mechanism to prove the validity of the resulted signature to any third party whenever necessary. Up to now, the security of many existing directed signatures was based on a single hard problem like factoring, discrete logarithm or elliptic curve discrete logarithm and these schemes appear secure today but in a near future, if an adversary finds a solution of these hard problems then the schemes will no longer be secure. Thus, the newly directed signature is developed to provide greater security level than that any directed signature schemes since it is impossible for the adversary to solve the two hard problems simultaneously. [ABSTRACT FROM AUTHOR]

Long spirals in the Euclidean plane have been introduced by A. Kurnosenko five years ago. Using a natural map of the shape sphere into the extended Gaussian plane we study spherical curves that are pre-images of plane long spirals. Loxodromes and spherical spiral antennas are typical examples of such spherical long spirals. The set of all planar spirals leaves invariant under an arbitrary similarity transformation. This set is divided in two disjoint classes by A. Kirnosenko. The first class is consist of the so-called short spirals which are widely used in geometric modeling. The second class of planar long spirals contains well-known logarithmic spiral and Archimedean spirals which have many applications in mathematics, astrophysics and industry. The notion of simplicial shape space is due to D. Kendall. The most popular simplicial shape space of order (2,3) is the set of equivalence classes of similar triangles in the plane. The sphere of radius 1/2 centered at the origin can be considered as a model of this quotient space, so-called the shape sphere. F. Bookstein and J. Lester showed that the one-point extension of the Euclidean plane, so-called the extended Gaussian plane, is another model of the same simplicial shape space. The present paper gives a description of long spirals on the shape sphere by the use a natural conformal mapping between two models. First, we examine long spirals in the extended Gaussian plane. After that, we describe some differential geometric properties of the shape sphere. Finally, we discuss parameterizations of long spirals on the shape sphere. [ABSTRACT FROM AUTHOR]

In this paper the authors combine the equicorrelation and equivariance test introduced by Wilks [13] with the likelihood ratio test (l.r.t.) for independence of groups of variables to obtain the l.r.t. of block equicorrelation and equivariance. This test or its single block version may find applications in many areas as in psychology, education, medicine, genetics and they are important 'in many tests of multivariate analysis, e.g. in MANOVA, Profile Analysis, Growth Curve analysis, etc' [12, 9]. By decomposing the overall hypothesis into the hypotheses of independence of groups of variables and the hypothesis of equicorrelation and equivariance we are able to obtain the expressions for the overall l.r.t. statistic and its moments. From these we obtain a suitable factorization of the characteristic function (c.f.) of the logarithm of the l.r.t. statistic, which enables us to develop highly manageable and precise near-exact distributions for the test statistic. [ABSTRACT FROM AUTHOR]

The basic processes affecting the cosmic ray (CR) transport in the heliosphere are combined in Parker's transport equation. However, adequate description of the relation between the modulation processes in the heliosphere and the profiles of the modulated GCR spectrum is a difficult task because the theoretical models should consider many parameters whose values are not known throughout the heliosphere. That is why the use of empirical and theoretical approximations is recommended, especially for calculation of CR's atmospheric effects and for practical tasks. A brief review is given of the most often used models for interpretation of cosmic ray data and prediction of particle fluxes. The force-field and diffusion-convection approximations to the cosmic ray transport equation, Moscow State University (MSU) model, Nagashima and Morishita, Badhwar and O'Neill's models, as well as Cosmic Ray Spectrum Approximation (CRSA) model, are discussed in the paper. The CRSA is compared to the Nagashima and Morishita's model equation and dependence between CRSA model parameters and time-lagged solar-heliospheric parameters for a given rigidity Pξ is derived. [ABSTRACT FROM AUTHOR]

The ITS-90 Inconsistency in overlap region of the Mercury-Gallium and the Water-Argon Sub-ranges are investigated in this paper. The calibration data of thirteen SPRTs are used to determine the magnitude of the inconsistency. The result shows it no greater than 0.22mK. By mean of extending a logarithm of the platinum resistance ratio of the ITS-90 interpolation in a power series, this paper gives an inconsistency function of the form of interpolation error in the region . The function is only with approximate error less than 3.4×10-5 mK, almost no error, checked by the SPRTs. [ABSTRACT FROM AUTHOR]

The Diffie-Hellman key exchange protocol is one of the well-known examples of public key cryptography which is based on the discrete logarithm problem (DLP): given integers g, h and n, find an integer a such that ga≡h(modn). In 2000, Ko, Lee et al. generalised the Diffie-Hellman protocol by using a class of algebraic structures called braid groups as platforms. Its security lies on the conjugacy search problem (CSP): given elements g and h in a group, find an element a in the group such that a-1ga = h. In this paper, we propose another key exchange protocol by using Chein loops-a subclass of Moufang loops. We shall discuss their potential as platforms for cryptosystems and their connection with the Ko-Lee et al. protocol. [ABSTRACT FROM AUTHOR]

This paper proposed an improvement of an existing signature scheme based on the hybrid of two problems. The security of this improved signature scheme is based on a hybrid of factorisation (FAC) and elliptic curve discrete logarithm problem (ECDLP). This improvement provides a higher level of security than the previous scheme. In the security evaluation, different aspects of attacks from adversaries are evaluated and the scheme showed that it is secured from those attacks. In the efficiency performance evaluation, the number of keys needed, the computational complexity and the communication cost are investigated. To date, these two problems have not yet been able to be solved simultaneously, making this signature scheme secure and efficient with minimal computational cost. [ABSTRACT FROM AUTHOR]

We prove that the generalized Morrey spaces are embedded between two generalized Stummel classes whose characteristics differ by a logarithmic factor. To this end, we prove a new property of Morrey spaces by showing that the generalized local Morrey spaces are embedded between weighted Lebesgue spaces with weights differing similarly only by a logarithmic factor. All the embeddings are sharp. We also give an equivalent norm for the generalized Stummel type spaces. [ABSTRACT FROM AUTHOR]

The multi-sample independence test for several groups of variables is a generalization of the usual independence test which is of great importance in several areas of application. The exact distribution of the likelihood ratio test statistic of this test, both in the real or complex multivariate Normal setting, has a non-manageable and complicated expression. Using a novel approach, we develop near-exact distributions for the distribution of the test statistic which are highly accurate and easy to use. These are obtained decomposing the null hypothesis of the test into two null hypotheses, one to test the equality of the several variance-covariance matrices and the other to test, assuming that the first null hypothesis is not rejected, the independence of several groups of variables. This procedure allows us to obtain, in a simple way, the likelihood ratio test statistic, the expression of its h-th null moment and the characteristic function of its logarithm. The decomposition of the null hypothesis induces a factorization of the characteristic function of the logarithm of the test statistic which enables the development of near-exact distributions. The near-exact distributions obtained have the form of mixtures of Generalized Near-Integer Gamma distributions revealing a height degree of precision in the approximation and good asymptotic properties for the different parameters involved. [ABSTRACT FROM AUTHOR]

The Hill estimator, the average of k excesses of ordered log-observations, can be regarded as the logarithm of the mean of order p = 0 of a set of adequate statistics. The mean of order p (MOP), now with p ≥ 0, of the same statistics leads to the so-called MOP extreme value index (EVI)-estimator, a simple generalisation of the classical Hill estimator of a positive EVI, recently introduced in the literature. This class of MOP EVI-estimators depends on the extra tuning parameter p ≥ 0, which makes it very flexible, and even able to overpass most of the 'classical' and even reduced-bias EVI-estimators. Apart from a simulation study that reflects such an assertion, we advance with a fully non-parametric double bootstrap algorithm for the choice of p and k. We further provide applications of the algorithm to simulated and real data in the fields of biostatistics. [ABSTRACT FROM AUTHOR]

We propose a mechanism that the soft supersymmetry breaking masses can be induced from the dynamical rearrangement of local U(1) symmetry in a five-dimensional model. The U(1) symmetry possesses several extraordinary features. The eigenstates of U(1) do not equal to those of boundary conditions. The U(1) charge of standard model particles does not equal to that of superpartners. A large U(1) charge hierarchy among superpartners and a standard model gauge singlet is necessary in order to obtain the masses of O(1)TeV. [ABSTRACT FROM AUTHOR]

Entanglement is one of the key features of the quantum mechanical systems that is fundamentally differen from a classical system, in consequence the dynamical behavior of entangled states is of a great significance. In this paper we investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to squeezed vacuum reservoirs with an arbitrary initial pure entangled state between two fields in the cavities. To estimate the degree of entanglement we use the logarithmic negativity. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state, the phase shift between them and the parameters of the squeezed vacuum reservoir. We derive the conditions, which assure that The states remain entangled although the interaction with the reservoir. The sudden death time of the entangled states is related to the squeezed parameter of the reservoir and the phase shift between the initial entangled states. [ABSTRACT FROM AUTHOR]

Cauchy problem for a quasi-linear abstract hyperbolic equation is considered, where the main operator is selfadjoint positive definite and represents a finite sum of its similar operators. For this problem the fourth order accuracy threelayer decomposition scheme is constructed on the basis of rational splitting of the cosine operator-function. To calculate the starting vectors necessary for its realization with the corresponding accuracy, we suggest a recursive algorithm, whose number of steps has the same order as the logarithm of division number of the time interval. [ABSTRACT FROM AUTHOR]

In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables. [ABSTRACT FROM AUTHOR]

One of the most important task of the Gamma-Ray Burst field is the calssification of the bursts. Many researches have proven the existence of the third kind (intermediate duration) of GRBs in the BATSE data. Recent works have analyzed BeppoSax and Swift observations and can also identify three types of GRBs in the data sets. However, the class memberships are probabilistic we have enough observed redshifts to calculate the redshift and spatial distribution of the intermediate GRBs. They are significantly farther than the short bursts and seems to be closer than the long ones. [ABSTRACT FROM AUTHOR]

The expression of survival factors for radiation damaged cells is based on probabilistic assumptions and experimentally fitted for each tumor, radiation and conditions. Here we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. A generalization of the exponential, the logarithm and the product to a non-extensive framework, provides a simple formula for the survival fraction corresponding to the application of several radiation doses on a living tissue. The obtained expression shows a remarkable agreement with the experimental data found in the literature, also providing a new interpretation of some of the parameters introduced anew. It is also shown how the presented formalism may have direct application in radiotherapy treatment optimization through the definition of the potential effect difference, simply calculated between the tumour and the surrounding tissue. [ABSTRACT FROM AUTHOR]