Slowly convergent innnite products Q 1 n=1 b n are considered, where fb n g is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the 'remainder' of the innnite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and eecient for some classes of sequences fb n g. For...

Reinforcement learning is an efficient method for solving Markov Decision Processes that an agent improves its performance by using scalar reward values with higher capability of reactive and adaptive behaviors. Q-learning is a representative reinforcement learning method which is guaranteed to obtain an optimal policy but needs numerous trials to achieve it. k-Certainty Exploration Learning Sy...

For spontaneous breaking of global or gauge symmetry, it is superfluous to assume that the vacuum expectation value of the scalar field manifesting the symmetry is nonvanishing. PACS Numbers: 11.30.Qc Electronic address: [email protected] 1 A crucial ingredient of the theories of spontaneous symmetry breaking is the assumption that the vaccum expectation value of the scalar field manifest...

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L1 = −∆+ V1 and L2 = −∆+ V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for D odd and ...

The following argument is adapted from that in Bell (1955). I cannot quite follow Bell’s argument1, so I have changed it to generate a result I understand. In outline, the result is as follows. We consider a classical theory given by a system of partial differential equations on a specified set of fields. Let Φ be the space of kinematically allowed fields. (In the general case, we may be dealin...

Introduction In spite of theoretical and experimental outstanding achievements, particle physics has not been able to reach a conclusion on the simple question: from which mechanism does mass originate ? It is a common belief that such a mechanism will be characterized by the observation of at least a scalar particle. Whether this object is elementary (SM or MSSM scenario), composite (technicol...

The spectrum of MSSM admits solitons carrying baryonic charge, or B-balls. In an inflationary universe they can be produced in significant numbers by a break-up of a scalar condensate along the flat directions. It is shown that if SUSY breaking is mediated to the observable sector by gravity, B-balls are unstable but decay to baryons and LSPs typically well below the electroweak phase transitio...

Mutation analysis inserts faults into a program to create test sets that distinguish the mutant from the original program. Inserted faults must represent plausible errors. Standard transformations can mutate scalar values such as integers, floats, and character data. Mutating objects is an open problem, because object semantics are defined by the programmer and can vary widely. We develop mutat...

In this letter, we introduce a new approach to formulate the family structure of the standard model. Trying to mimic the highly contrained representation structure of the standard model while extending the symmetry, we propose a SU (4) H ⊗ SU (3) C ⊗ SU (2) L ⊗ U (1) X model which upon symmetry breaking gives the three-family standard model, with the Higgs supermultiplets for incoporating super...

We derive the propagator for a massless, minimally coupled scalar on a D-dimensional, spatially flat, homogeneous and isotropic background with arbitrary constant deceleration parameter. Our construction uses the operator formalism, by integrating the Fourier mode sum. We give special attention to infrared corrections from the nonzero lower limit associated with working on finite spatial sectio...