Abstract:
to perform a more transparent analysis of the problems raised by contrary inferences within consistent history approach to quantum theory, we extend the formalism of the conceptual basis. according to our analysis, the conceptual difficulties arising from contrary inferences are ruled out.

Abstract:
This paper gives the concept of the contrary orthogonal matrix and studies its centrosymmetry, and obtains the following main results: the contrary orthogonal matrix is row column symmetric matrix and centrosymmetric matrix; cross the row anyway, the matrix transpose matrix and its transpose rows and columns transposed matrix is centrosymmetric matrix; cross the row anyway, rows of the matrix transpose inverse of a matrix of rows equal to its inverse transpose, the transpose column inverse of a matrix is equal to its inverse columns of the matrix transpose; its row transpose matrix transpose is equal to its transpose rows of the matrix transpose, its columns of transpose matrix is equal to its transpose matrix of columns.

Abstract:
The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are briefly analyzed.

Abstract:
Euclidean geometry consists of straightedge-and-compass constructions and reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. We consider three versions of Euclid's parallel postulate: Euclid's own formulation in his Postulate 5; Playfair's 1795 version, and a new version we call the strong parallel postulate. These differ in that Euclid's version and the new version both assert the existence of a point where two lines meet, while Playfair's version makes no existence assertion. Classically, the models of Euclidean (straightedge-and-compass) geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to the different versions of the parallel axiom. In this paper, we completely settle the questions about implications between the three versions of the parallel postulate: the strong parallel postulate easily implies Euclid 5, and in fact Euclid 5 also implies the strong parallel postulate, although the proof is lengthy, depending on the verification that Euclid 5 suffices to define multiplication geometrically. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions.

Abstract:
The Luders postulate is reviewed and implications for quantum algorithms are discussed. A search algorithm for an unstructured database is described.

Abstract:
Many authors noted that the principle of relativity together with space-time homogeneity and isotropy restrict the form of the coordinate transformations from one inertial frame to another to being Lorentz-like. A free parameter in these equations, $k$, plays the part of $c^{-2}$ in special relativity. It is usual to claim that $k$ is determined by experiment and hence, that special relativity does not need the postulate of constancy of the speed of light. I analyze how one would go about determining $k$ empirically and find that all methods suffer from severe problems without further assumptions, none as simple and elegant as the postulate of constancy of the speed of light. I conclude that while the formal structure of the transformation equations can be determined without appeal to the second postulate, the theory is left without physical content if we ignore this postulate. Specifically, evaluating $k$ requires creating a signal that travels identically in opposite directions or ensuring that such a signal exists. Assuming this property about light is sufficient to obtain special relativity, although the condition is logically weaker than Einstein's postulate of the constancy of the speed of light. The physical core of the second postulate, therefore, lies in its assurance of the isotropy of some signal.

Abstract:
Many authors noted that the principle of relativity together with space-time homogeneity and isotropy restrict the form of the coordinate transformations from one inertial frame to another to being Lorentz-like. The equations contain a free parameter, $k$ (equal to $c^{-2}$ in special relativity), which value is claimed to be merely an empirical matter, so that special relativity does not need the postulate of constancy of the speed of light. I analyze this claim and argue that the distinction between the cases $k = 0$ and $k \neq 0$ is on the level of a postulate and that until we assume one or the other, we have an incomplete structure that leaves many fundamental questions undecided, including basic prerequisites of experimentation. I examine an analogous case in which isotropy is the postulate dropped and use it to illustrate the problem. Finally I analyze two attempts by Sfarti, and Behera and Mukhopadhyay to derive the constancy of the speed of light from the principle of relativity. I show that these attempts make hidden assumptions that are equivalent to the second postulate.

Abstract:
According to the widely accepted notion, the Schr{\"o}dinger equation (SE) is not derivable in principle. Contrary to this belief, we present here a straightforward derivation of SE. It is based on only two fundamentals of mechanics: the classical Hamilton-Jacobi equation(HJE) and the Planck postulate about the discrete transfer of energy at micro-scales. Our approach is drastically different from the other published derivations of SE which either employ an ad hoc underlying assumption about the probabilistic or the statistical nature of the micro-scale phenomena, or rely on the prior knowledge of SE and arrive at it by introducing a new postulate - neither present in classical mechanics nor following from experiments - with a suitable but physically unjustifiable choice of a key arbitrary constant.