The Smoothed Particle Hydrodynamics (SPH) method suffers from the presence of irregular particle distributions inherent in its Lagrangian nature. A way to circumvent this problem is consider a quasi-Lagrangian SPH scheme and use Shifting Technique (PST). In framework, we include an approximate Riemann solver represent interaction obtain two different Riemann-based schemes: one mass-constant mod...

One of the basic geometric objects in conformal field theory (CFT) is the moduli space of Riemann surfaces whose boundaries are “rigged” with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations. We generalize this picture to quasisymmetric boundary parametrizations. By using tools such as the extended λ-lemma and conformal welding we pr...

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces a Hilbert space. We impose natural symmetry condition on the that corresponds to considering an important class into symmetric and k-symmetric spaces. Using appropriate description such we obtain new results for corresponding extended solutions, including how primitive certain unitary ...

A class of extended vector fields, called extended divergence-measure fields, is analyzed. These fields include vector fields in Lp and vector-valued Radon measures, whose divergences are Radon measures. Such extended vector fields arise naturally in the study of the behavior of entropy solutions to the Euler equations for gas dynamics and other nonlinear systems of conservation laws. A new not...

The main goal of this study is to demonstrate an existence result a coupled implicit Riemann-Liouville fractional integral equation. First, we prove new fixed point theorem in spaces with extended norm structure. That generalized Darbo’s associated the vector Kuratowski measure noncompactness. Second, employ our obtained investigate solutions equation on Banach space C([0,1],R)×C([0,1],R).

We present a high resolution, finite-volume Cartesian grid method for simulating potential explosions in nuclear containment structures. The basic method is a Godunov-type method that relies on the solution to non-linear Riemann problems at the interfaces between cells of a uniform Cartesian mesh. We have extended these methods to general quadrilateral and hexahedral adaptively refined grids. T...

The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for th...

This algorithm was proposed in 70’s. Miller and Rabin gave two versions of the same algorithm to test whether a number n is prime or not. Whereas Rabin’s algorithm works with a randomly chosen a ∈ Zn, and is therefore a randomized one, Miller’s version tests deterministically for all a’s, where 1 ≤ a ≤ 4 log n. But correctness of Miller’s algorithm depends on correctness of Extended Riemann Hyp...

Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities...

Abstract. A model with a scalar type eight-fermion interaction is investigated in curved spacetime. The ground state of the model can be obtained by observing the effective potential. Applying the Riemann normal coordinate expansion, we calculate an effective potential of the model in a weakly curved spacetime. The result is extended to models with multi-fermion interactions. We numerically sho...