Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix eleme...

The number of substitutions (of nucleotides, amino acids, etc.) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random vari...

CafeOBJ is a wide spectrum formal specification language based on multiple logical foundations: mainly initial and hidden algebra. A wide range of systems can be specified in CafeOBJ thanks to its multiple logical foundations. However, distributed real-time systems happen to be excluded from targets of CafeOBJ. In this paper, we propose a method of modeling and verifying such systems based on C...

The long-standing problem of nding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and parameterized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state f...

Addressing a perennial apologetic and pastoral demand, the twelve Minor Prophets undertake to assert and demonstrate the goodness of God in the face of apparent evidence to the contrary. I will argue that the Twelve were intended to be read together and have the purpose of encouraging the post-exilic reader to trust Yahweh’s faithfulness to his salvation promises, even in the face of the many s...

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The strongly interacting matter under extreme conditions of temperature for the conjectured deconfined phase of the quark-gluon plasma is investigated. A systematic study of the form of the thermal ratio of the disorder deviation (TRDD) is presented with the emphasis on the degree of deviation of the TRDD-function from unity. The space-time evolution of quarks and gluons is studied in the frame...

The cheongsam, the typical national apparel of the internal and external harmonious unity, is known as the representative of the Chinese clothing culture. It has expressed the virtuous, elegant, and gentle temperament of the Chinese women through flowing melody, rakish picturesque conception, and strong poetic emotion. The paper studies several aspects of the origin, evolution, techniques and c...