In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

in this paper, we show that the conditional transform with respect to the gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. we then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

In this work, regularity of $n$-generalized Schützenberger product monoids from the point Group Theory is studied. Here, it determined necessary and sufficient conditions $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ to be regular while all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ are monoids. Also, by considering groups, given another result for product.

In this paper we propose higher-order rewrite systems without bound variables. In order to prove their connuence under the assumption of orthogonality, we study a simple proof method which employs a characterization of the diamond property of a parallel reduction. By an application of the proof method, we obtain a new connuence result for orthogonal higher-order conditional rewrite systems.

Abstract. Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman trans...

In this paper, Universal any and Negative Polarity Item any are uniformly analyzed as ‘counterfactual’ donkey sentences (in disguise). Their difference in meaning is reduced here to the distinction between strong and weak readings of donkey sentences. It is shown that this explains the universal and existential character of Universaland NPI-any, respectively, and the positive and negative conte...

This Communication reports a low-temperature diamond synthesis technique, in which diamonds (10-250 mum) can form at a temperature as low as 440 degrees C by reduction of dense CO2 with metallic Na. The X-ray diffraction pattern of a powder sample shows three reflection peaks, indexed with 111, 220, and 311, corresponding unambiguously to cubic diamond. The Raman spectrum of the product exhibit...