The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.Comment: 13 pages, accepted for publication in Found. Phys. arXiv admin note: substantial text overlap with arXiv:1107.227

PROBLEMS OF THE EXPRESSION OF CONDITIONAL RELATIONSHIPS IN THE UZBEK LANGUAGE

The article is aimed at investigating the problems of the expression of conditionals in the Uzbek language. Particularly, in the article a special emphasis is placed on the analysis of peculiarities of formal expressions of conditionals in the Uzbek language. The objectives of the research are formed by defining the notion of condition in Uzbek, studying the forms of expression of the conditionals, analyzing the syntactic structure of the conditional constructions, identifying the levels of language in which conditionals are expressed, analyzing the functions of conjunctions connecting the clauses of conditional sentences and identifying the stylistic features of conditional conjunctions. Linguistic description, generalization of prior ideas and theories in the field and componential analysis methods are used. The results of the study have shown that the conditionals are expressed by the synthetic and analytic forms, the synthetic forms (conditionals formed by affixes) refer to the conditional forms constructed by adding the conditional affix “-sа” to the stem of the verb, the analytic forms (the combination with two or more components) include the form of“-sа”+ to’liqsiz fe’l (an auxiliary verb (edi, ekan, emish), the combination of a part of speech which is not a verb+bo’l (to be)+sa, lexical units as desa, bo’lsa, yo’qsa and proverbs. The conditionals are mainly expressed at the grammatical and lexical levels of the language. In the grammatical layer, the conditionals are especially expressed through a syntactic unit which is a complex sentence and it is important to note the role of the conditional affix “-sa” in expressing a conditionat the morphological level. In the lexical layer, some lexical units and proverbs can be regarded as means of expressing conditionality. Also,conditional clauses are connected by various conjunctions (agar, basharti, mabodo, bordiyu, madomiki all referring to “if” in English) and these connectives possess different stylistic colorings and the main function of such conjunctions is not to express conditionality, but to emphasize and exaggerate a conditional meaning. So, the structural peculiarities of conditionals in Uzbek are determined by their syntactic structure, their expression in different language levels and the conditional conjunctions

Abstract structures for moods in Greek

It is my intention to make two major points in this paper: 1. The first has to do with finding a frame within which the modal expressions of one particular Ancient IE [Indoeuropean] language – I have chosen Classical Greek – can be best described. I shall try to point out that the regularities which we find in these expressions must depend on an underlying principle, represented by abstract structures. These structures are semanto-syntactic, which means that the semantic properties or bundles of properties are arranged not in a linear order but in a hierarchical order, analogous to a bracketing in a PS structure. The abstract structures we propose have, of course, a very tentative character. They can only be accepted as far as evidence for them can be furnished. 2. My second point has to do with the modal verb forms that were the object of the studies of most Indo-Europeanists. If in the innermost bracket of a semanto-syntactic structure two semantic properties or bundles of properties can be exchanged without any further change in the total structure, and if this change is correlated with a change in verbal mood forms and nothing else, then I think we are faced with a case where these forms can be said to have a meaning of their own. I shall also try to show how these meanings are to be understood as bundles of features rather than as unanalyzed terms. In my final remarks: I shall try to outline the bearing these views have on comparative IE linguistics

Marginal distributions for cosmic variance limited CMB polarization data

We provide computationally convenient expressions for all marginal distributions of the polarization CMB power spectrum distribution P(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set of ensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT, sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specific polarization CMB power spectra. This distribution describes the CMB power spectrum posterior for cosmic variance limited data. The expressions derived here are general, and may be useful in a wide range of applications. Two specific applications are described in this paper. First, we employ the derived distributions within the CMB Gibbs sampling framework, and demonstrate a new conditional CMB power spectrum sampling algorithm that allows for different binning schemes for each power spectrum. This is useful because most CMB experiments have very different signal-to-noise ratios for temperature and polarization. Second, we provide new Blackwell-Rao estimators for each of the marginal polarization distributions, which are relevant to power spectrum and likelihood estimation. Because these estimators represent marginals, they are not affected by the exponential behaviour of the corresponding joint expression, but converge quickly.Comment: 8 pages, 3 figures; minor adjustment, accepted for publication in ApJ