Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to ‎obtain a‎ ‎general‎ relation for casimir entropy and ‎i‎nternal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and ‎the‎ electromagnetic field. For this purpose, using Lagrangian and based on a perturb...

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...

Conditional branches are expensive. Branches require a signi cant percentage of execution cycles since they occur frequently and cause pipeline ushes when mispredicted. In addition, branches result in forks in the control ow, which can prevent other code-improving transformations from being applied. In this paper we describe pro le-based techniques for replacing the execution of a set of two or...

1. Suppose that the matrix Mk is of dimension nk × nk+1, k ∈ {1, . . . , h}. We wish to compute the product M1M2 · · ·Mh. Notice that the order of multiplication makes a difference. For example, if (n1, n2, n3, n4) = (1, 10, 1, 10), the calculation (M1M2)M3 requires 20 scalar multiplications, but the calculation M1(M2M3) requires 200 scalar multiplications. Indeed, multiplying a m × n matrix by...

The class of non-homogeneous operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. The method is based on expressing a first order non-homogeneous differential operator as a product of a scalar function, a differential operator, and the reciprocal scalar function.

The class of non-homogeneous operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spasces, are shown to be isomorphic to each other. The method is based on expressing a first order non-homogeneous differential operator as a product of a scalar function, a differential operator, and the reciprocal scalar function.

We consider the Krein realization of the Hilbert space for a massless scalar field in 1+1 dimensions. We find convergence criteria and the completion of the space of test functions S with the topology induced by the Krein scalar product. Finally, we show that the interpretation for the Fourier components as probability amplitudes for the momentum operator is lost in this case.

We study phenomenologically the invariant mass spectra of scalar dipion states produced in cascade decays of excited Υ and ψ, and J/ψ decays into light vector mesons. The dipion production amplitude is given as a product in the Born term and an effective scalar form factor written in terms of a unitarized chiral theory. The model reproduces the experimental mass spectra very well. @ @ @ @ @ @@ @ @