In this paper, we , rst establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some MIDPOINT type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.

Imprecise measurement tools produce imprecise data. Interval-valued data is usually used to deal with such imprecision. So interval-valued variables are used in estimation methods. They have recently been modeled by linear regression models. If response variable has any statistical distributions, interval-valued variables are modeled in generalized linear models framework. In this article, we propose a new consistent estimator of a parameter in generalized linear models with regard to distributions of response variable in the exponential family. A simulation study shows that the new estimator is better than others on the basis of particular distributions of response variable. We present optimal properties of the estimators in this research

In this study, we first establish two new identities for multiplicative differentiable functions. Based on these identities, we derive the MIDPOINT and trapezoid type inequalities. The acquired outcomes improve and refine upon Khan and Budak's findings. At the conclusion, some applications to special means are provided.

Having knowledge about elastic prosperities of different layers of Earth has many useful applications in geophysical and geotechnical engineering projects. One of the important parameters in determination of static constants and the key parameter controlling the amplification of seismic motion during earthquake is shear-wave velocity. Because of the dispersive characteristic of Rayleigh waves when traveling through a layered medium and the important role of Swave velocity in determination of Rayleigh wave velocity, dispersion of phase velocity of surface waves can be used for near-surface S-wave delineation. In this study Common Mid Point Cross-Correlation analysis of multi-channel surface-wave data (CMPCC MASW method) is used for dispersion curve determination of 2-D seismic reflection survey data. CMPCC MASW analysis is a further extension of Multi-channel Analysis of Surface Waves (MASW) that improves the accuracy and resolution of MASW by overcoming the problem of improved lateral resolution trading off against accuracy of phase velocity at low frequencies. It also enables Spectral Analysis of Surface Waves (SASW) method to perform a pseudo multi-channel analysis in order to distinguish fundamental mode from higher modes visually and therefore solving the spatial aliasing problem of SASW method.

We first construct new Hermite-Hadamard type inequalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and MIDPOINT type results involving generalized fractional integrals for functions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.

In this work four algorithms are presented for the integration of equations governing the behavior of von Mises material in plastic limit. Two of them are single-step and the others are double-step algorithms. Single-step algorithms are straight forward extension of backward Euler method or MIDPOINT RULE while double-step algorithms are a combination of two. In past similar algorithms were proposed for special cases of isotropic / kinematic hardening; however the algorithms presented in this work are applicable to general isotropic/kinematic hardening laws. Theoretical as well as numerical aspects are presented for all integration schemes and elaborated for double-step algorithms which are less explored in the literature. A comparison is made between the presented algorithms and the classical backward Euler method.

As we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we dene the concepts of MIDPOINT and radius functions for a fuzzy number, MIDPOINT and radius vectors for a fuzzy number vector and MIDPOINT and radius systems for a fuzzy linear system. All these new definitions are defined based on the parametric form of fuzzy numbers. Then, by these new concepts, we propose a simple method to solve a fuzzy linear system and obtain it's algebraic solution. Also, we present a sufficient condition for the obtained solution vector to be always a fuzzy vector. Finally, several numerical examples are given to show the efficiency and capability of the proposed method.

As a result of RULE of law ideal, judges are required to act in accordance with laws. The ideal is justified by some political values: political liberty, legal liberty, personal liberty and equality. Citizens are subject only to the law not to the arbitrary will or judgment of another who wields coercive government power. But in some cases law is indeterminate. In these cases there is an important question: how can the law command when the law books are silent or unclear or ambiguous? There are three theory in jurisprudence: legal positivism, legal pragmatism and legal interpretivism. I reject positivism and pragmatism and urge interpretivism. I believe that it provides a better account of our law.