On the stability of the generalized Cauchy–Jensen set-valued functional equations

In this paper, we prove the Hyers–Ulam–Rassias stability of the generalized Cauchy–Jensen set-valued functional equation defined by

$$\begin{aligned} \alpha f\left( \frac{x+y}{\alpha } + z\right) = f(x) \oplus f(y)\oplus \alpha f(z) \end{aligned}$$

for all \(x,y,z \in X\) and \(\alpha \ge 2\) on a Banach space by using the fixed point alternative theorem.

     

Asymptotic approximation of kernel-type estimators with its application

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.     

Nonzero solutions for a system of variational inequalities in reflexive Banach spaces

In this paper, some existence theorems of nonzero solutions for a system of bilinear variational inequalities are proved by using the coincidence degree theory in reflexive Banach spaces. The results presented in this paper improve and extend some known results in the literature.     

New exact travelling wave solutions of Kawahara type equations

The Auxiliary equation method is used to find analytic solutions for the Kawahara and modified Kawahara equations. It is well known that different types of exact solutions of the given auxiliary equation produce new types of exact travelling wave solutions to nonlinear equations. In this paper, new exact solutions of the auxiliary equation are presented. Using these solutions, many new exact travelling wave solutions for the Kawahara type equations are obtained.     

Butson Hadamard matrices with partially cyclic core

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value ?1 within LCZ.     

Lifting up an infinite chain of prime ideals to a valuation ring

We prove that for an arbitrary chain of prime ideals in an integral domain, there exists a valuation domain which has a chain of prime ideals lying over .

     

Effect of hydrostatic pressure on closed-loop phase behavior of block copolymers

The effect of hydrostatic pressure (P) on closed-loop phase behavior of deuterated polystyrene-block-poly(n-pentyl methacrylate) copolymers [dPS-PnPMA] was investigated by using small-angle neutron scattering and birefringence. For P<20.7 bar, dPS-PnPMA exhibited a lower disorder-to-order transition temperature (T(LDOT)) at 175 degrees C, and then an upper order-to-disorder transition temperature (T(UODT)) at 255 degrees C. With increasing pressure both T(LDOT) and T(UODT) were markedly changed, where dT(LDOT)/dP was 725 degrees C/kbar and dT(UODT)/dP was -725 degrees C/kbar. These are consistent with predictions by the Clausius-Clapeyron equation using measured values of the volume and enthalpy changes of both transitions. The large pressure coefficients imply that the closed-loop phase behavior observed for PS-PnPMA is an entropic-driven phase transition.     

Observation of B0-->pLambda(pi)(-)

We report the first observation of the charmless hyperonic B decay, B0-->pLambda(pi)(-), using a 78 fb(-1) data sample recorded on the Upsilon(4S) resonance with the Belle detector at KEKB. The measured branching fraction is B(B0-->pLambda(pi)(-))=(3.97(+1.00)(-0.80)+/-0.56)x10(-6). Searches for B0-->pLambda(K)- and pSigma(0)pi(-) yield no significant signals and we set 90% confidence-level upper limits of B(B0-->pLambda(K)-)<8.2x10(-7) and B(B0-->pSigma(0)pi(-))<3.8x10(-6).     

A single current density component imaging by MRCDI without subject rotations

Magnetic resonance current density imaging (MRCDI) is a useful method for measuring electrical current density distribution inside a subject. Due to the requirement of subject rotations in MRCDI, MRCDI has not been widely applied to in vivo studies. In this paper, we propose a new current density image (CDI) reconstruction method by which a single component of the current density can be imaged by MRCDI without subject rotations. After measuring one of the two magnetic field components, produced by the current density component passing through the measurement plane, we have reconstructed the current density component images in the spatial frequency domain. Even though the proposed method has a limitation that the area of magnetic field measurement should be much larger than that of the current density, the proposed method is expected to expedite MRCDI applications to in vivo studies.     

System size and centrality dependence of charged hadron transverse momentum spectra in Au + Au and Cu + Cu collisions at square root of SNN = 62.4 and 200 GeV

We present transverse momentum distributions of charged hadrons produced in Cu + Cu collisions at square root of SNN = 62.4 and 200 GeV. The spectra are measured for transverse momenta of 0.25 < pT < 5.0 GeV/c at square root of SNN = 62.4 GeV and 0.25 < pT < 7.0 GeV/c at square root of SNN = 200 GeV, in a pseudorapidity range of 0.2 < eta < 1.4. The nuclear modification factor R(AA) is calculated relative to p + p data at both collision energies as a function of collision centrality. At a given collision energy and fractional cross section, R(AA) is observed to be systematically larger in Cu + Cu collisions compared to Au + Au. However, for the same number of participating nucleons, R(AA) is essentially the same in both systems over the measured range of pT, in spite of the significantly different geometries of the Cu + Cu and Au + Au systems.