Narrow Results

Because of the problems arising from the fermion unification in the traditional grand unified theory and the mass hierarchy between the four-dimensional Planck scale and weak scale, we suggest the low energy gauge unification theory with low high-dimensional Planck scale. We discuss the nonsupersymmetric SU(5) model on M⁴ × S¹/Z₂ × S¹/Z₂ and the supersymmetric SU(5) model on M⁴ × S¹/(Z₂ × Z₂′) × S¹/(Z₂ × Z₂′). The SU(5) gauge symmetry is broken by the orbifold projection for the zero modes, and the gauge unification is accelerated due to the SU(5) asymmetric light KK states. In our models, we forbid the proton decay, still keep the charge quantization, and automatically solve the fermion mass problem. We also comment on the anomaly cancellation and other possible scenarios for low energy gauge unification.

We calculate the lowest order quantum gravity contributions to QED beta function in an effective field theory picture with a momentum cutoff. We use a recently proposed four-dimensional improved momentum cutoff that preserves gauge and Lorentz symmetries. We find that there is nonvanishing quadratic contribution to the photon two-point function but that does not lead to the running of the original coupling after renormalization. We argue that gravity cannot turn gauge theories asymptotically free.

A geometric interpretation of the reciprocity relation of the Selberg integral is given. Combinatorial topological properties of the point-configuration spaces are used. It has an application to the conformal field theory.

We investigate the gauge dynamics of nonsupersymmetric SU(N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

Using the properties of the partition function for a Yang–Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.

This paper deals with the study of the reliability of multicomponent stress–strength model assuming that the strength components are independently and identically distributed as power transformed half-logistic (PHL) distribution. The strength components which are subject to a common stress are assumed to be independent with either Weibull distribution or PHL distribution. The maximum likelihood estimates of the multicomponent stress–strength reliability and its asymptotic confidence interval under the above said conditions are obtained. The Bayes estimates of the multicomponent stress–strength reliability are also obtained under squared error loss function and using gamma priors for the parameters. To evaluate the performance of the procedure, a simulation study is considered. For illustration purpose of the proposed model, two real life examples are given.

Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

The incomplete Beta function $B(a,b;x)$ is defined for $a,b>0$ and $0<x<1$. This definition was extended to negative integer values of $a$ and $b$ by Özçaḡ et al. using neutrix limits. Partial derivatives of the incomplete Beta function $B(a,b;x)$ for negative integer values of $a$ and $b$ were then evaluated. In the following, a number of results are obtained for the incomplete Beta function $B(a,b;x)$ and then the corresponding results for the Beta function $B(a,b)$ are deduced.

Due to their wide range of applications in many areas of modern analysis, the splendid Hermite–Hadamard inequalities for convex function are very attractive for researcher community. Many authors have been working on their variants, refinements and extensions. The aim of this research is to establish a novel identity and Hermite–Hadamard-type inequalities for convex functions linked with the renowned conformable integral operators. We have pointed some particular cases of the results obtained here in order to show that they reduce some well-known results to relatively simple ones.

In this research paper, we generalized the results of Ignacy in the multivariate case in order to characterize the complex Wishart distribution.

We give an approximation formula to the drain time of the draining tank problem for an incompressible and nonviscous liquid with an unsteady flow effect. One can approximate the unsteady flow effect by elementary functions, and it is suitable for university students to learn Bernoulli’s equation with the unsteady flow effect.