In this research, we have studied of thymine dimer binding on the relative energies and dipole moment values and the structural properties of solvent effect (water, methanol and ethanol) surrounding single-walled and multi walled carbon nanotube, by using QM/MM simulation, those **calculations** have carried out with the Gaussian and Hyper Chem package. In this study we investigated the polar solvents effects on SWCNT within the Onsager self - consistent reaction field (SCRF) model using a Hartree-Fockmethod and the temperature effect on the stability of SWCNT in various. Because some of the Physicochemical parameters related to structural properties of SWCNT, we used different force fields to determine energy and other types of geometrical parameters, on the particular SWCNT, Because of the differences among force fields, the energy of a molecule calculated using two different force fields will not be the same. It is important to understand the energetic, stability dependent physical properties of armchair (m, n) carbon nanotube. In this study, the difference in force fields illustrated by comparing the calculated energies by using force fields such as AMBER ,MM+, and BIO+ .The **quantum** **Mechanics** **calculations** were carried out with the GAUSSIAN 98 program based on density functional theory (DFT) at the B1LYP/6-31G* level. Normal Mode Analysis is an important tool for studying the structure and dynamics of Nano-sized systems. The vibrational frequencies obtained can be used to relate observed spectra to the details of the molecular structure, dynamics and other thermodynamic properties.

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So, The structure ofSWCNT as well as their dipole moments and relative energies have been studied by molecular dynamics simulation and **quantum** **mechanics** **calculations** within the Onsager self - consistent reaction field (SCRF) model using a Hartree-Fockmethod (HF) at the HF/3-21G level and the structural stability of considered nanotube in different solvent media and temperature have been compared and analyzed.We investigate effects of water, methanol and a mixture of them on interaction of Temozolomide with SWCNT, utilizing these force fields too 48-66 .

So, The structure of SWCNT as well as their dipole moments and relative energies have been studied by molecular dynamics simulation and **quantum** **mechanics** **calculations** within the Onsager self - consistent reaction field (SCRF) model using a Hartree-Fock method (HF) at the HF/3-21G level and the structural stability of considered nanotube in different solvent media and temperature have been compared and analyzed. The **calculations** have been done with the GAUSSIAN 98 program according to Hartree-Fock (HF) theory at the HF/ STO-3G level. Gibbs free energy, enthalpy, entropy and dipole moment values are compared in gas phase, water and methanol, in this research. II-computational details

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Abstract. Are the standard laws of Physics really fundamental principles? Does the physical vacuum have a more primordial internal structure? Are quarks, leptons, gauge bosons... ultimate elementary objects? These three basic questions are actually closely related. If the deep vacuum structure and dynamics turn out to be less trivial than usu- ally depicted, the conventional "elementary" particles will most likely be excitations of such a vacuum dynamics that remains by now unknown. We then expect relativity and **quantum** **mechanics** to be low-energy limits of a more fundamental dynamical pattern that generates them at a deeper level. It may even happen that vacuum drives the expan- sion of the Universe from its own inner dynamics. Inside such a vacuum structure, the speed of light would not be the critical speed for vacuum constituents and propagating signals. The natural scenario would be the superbradyon (superluminal preon) pattern we postulated in 1995, with a new critical speed c s much larger than the speed of light

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In §1.2 the basic elements of **quantum** probability are reviewed, and contrasted with the joint probability structure of classical systems. The split between **quantum** and classical probability is then analysed in terms of "conditional probabilities" in §1.3, based on and extending some recent work [Hall, 1989, §2]. It becomes necessary to distinguish and discuss two possible formulations of these conditionals, labelled as "transitional" and "static" formulations. While the transitional formulation is relevant in connection with modelling "transition probabilities" in **quantum** **mechanics**, I shall argue that it brings in conceptual elements irrelevant to assessing fundamental distinctions between classical and **quantum** probability (in particular, a discussion of models of measurement becomes necessary). Hence this formulation is rejected in favour of the static formulation and the difference between classical and **quantum** probability examined within the context of the latter. This difference is characterised in terms of one of the basic laws of classical probability theory (the "contradictory inference" p(A |B) + p (A '|B ) = 1 ), which must be modified for **quantum** probability. This modification is interpreted as modelling the complementary properties of **quantum** systems.

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Chapter 4 is dedicated to the problem of neutrino transport. Carefully ac- counting for neutrino transport is an essential component of many astrophys- ical studies particularly in supernovae and collisions of neutron stars. Solving the full transport equation is too expensive for most realistic applications, es- pecially those involving multiple spatial dimensions. For such cases, resorting to approximations is often the only viable option for obtaining solutions. One such approximation, which recently became popular, is the M1 method. It utilizes the system of the lowest two moments of the transport equation and closes the system with an ad hoc closure relation. The accuracy of the M1 solution depends on the quality of the closure. Several closures have been proposed in the literature and have been used in various studies. We perform an extensive study and quantitative comparison of these closures We compare the results of M1 **calculations** with precise Monte Carlo **calculations** of the ra- diation field around spherically-symmetric protoneutron star models. We find that no closure performs consistently better or worse than others in all cases. The level of accuracy of a given closure depends on the matter configuration, neutrino type, and neutrino energy. Given this limitation, the maximum en- tropy closure by Minerbo yields accurate results in the broadest set of cases considered in this work.

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The first relationship between **quantum** and classical vari- ables is due to Ehrenfest @28# who showed that the equation of motion for the average values of **quantum** observables coincides with the corresponding classical expression. ~Sur- prisingly, the first mathematically rigorous treatment on the subject was not carried out until as late as 1974, see Ref. @29#.! Ehrenfest’s result leads to the mean-field approach, where classical dynamics is coupled to the evolution of the expectation values of **quantum** variables @30–33#. The mean- field equations of motion possess all of the properties of the purely classical equations and are rigorous insofaras the mean values of **quantum** operators are concerned. However, an expectation value does not provide information about the outcome of an individual process. The mean-field approach gives a satisfactory description of the classical subsystem as long as changes within the **quantum** part are fast compared to the characteristic classical time scale. If classical trajectories depend strongly on a particular realization of the **quantum** evolution, the mean-field approximation is inadequate. The problem can be corrected, for instance, by the introduction of stochastic **quantum** hops between preferred basis states, which define classical potential energy surfaces, with prob- abilities determined by the usual **quantum**-mechanical rules @34–36#. The decoherent histories interpretation of **quantum** **mechanics** @37,38# formulated on the level of individual his- tories @39,40# establishes a theoretical foundation of the sur- face hopping technique @41#.

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Using the 4-geon model, an orthomodular lattice of propositions, characteristic of quantum mechanics, is formally constructed within the framework of classical general relativity.. The m[r]

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Abstract: The EPR paradox is known as an interpretive problem, as well as a technical discovery in **quantum** **mechanics**. It defined the basic features of two-**quantum** entanglement, as needed to study the relationships between two non-commuting variables. In contrast, four variables are observed in a typical Bell experiment. This is no longer the same problem. The full complexity of this process can only be captured by the analysis of four-**quantum** entanglement. Indeed, a new paradox emerges in this context, with straightforward consequences. Either **quantum** behavior is capable of signaling non-locality, or it is local. Both alternatives appear to contradict existing knowledge. Still, one of them has to be true, and the final answer can be obtained conclusively with a four-**quantum** Bell experiment.

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We’ve seen that either of two related packages of assumptions — given in (a) and (b) of Theorem 2 — lead in a very simple way the homogeneity and self-duality of the space E(A) associated with a probabilistic model A, and hence, by the Koecher-Vinberg Theorem, to A’s having a euclidean Jordan structure. While this is not the only route one can take to deriving this structure (see, e.g, [27] and [31] for approaches stressing symmetry principles), it does seem especially straightforward. As discussed in the introduction, several other recent papers (e.g, [20, 28, 14, 25, 11]) have derived standard finite-dimensional **quantum** **mechanics**, over C, from operational or information- theoretic axioms. Besides the fact that the mathematical development here is quicker and easier, the axiomatic basis is considerably different, and arguably leaner, making no appeal to the struc- ture of subsystems, or to the isomorphism of systems with the same information-carrying capacity, or to local tomography. The last two points are particularly important: by avoiding local tomog- raphy, we allow for real and quaternionic **quantum** systems; by not insisting that physical systems having the same information capacity be isomorphic, we allow for **quantum** theory with supers- election rules, and for physical theories in which real and quaternionic systems can coexist. Of course, the door has been opened a bit wider than this: our postulates are also compatible with spin factors and with the exceptional Jordan algebra. 10

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In doing so, Bohm had reformulated **quantum** **mechanics** by describing the particle classical trajectory by a **quantum** Hamilton-Jacobi equation while retaining the **quantum** aspect of the particle. Thus, his formulation includes some hidden variables that also describe the state of the particle. The particle is described by the action S that satisfies the Hamilton-Jacobi equation, and R satisfying the continuity equation. In the framework of this recipe, a classical spin potential is derived whose force yields a viscous force. The coeﬃcient of viscosity is found to be directly proportional to the spin.

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IMW is not the most popular interpretation of **quantum** theory between physicians but its popularity appar- ently increases. Most of all the supporters of IMW are in the **quantum** cosmology and in **quantum** computation. In **quantum** cosmology it is possible to research the Universe, avoiding the difficulty of the standard interpreta- tion with the external observer. In **quantum** computation the key advantage is that the parallel computations are realized by the same computer; it enters in the main picture of IMW. Moreover, the advantage of IMW in quan- tum **mechanics** is that it permits to consider **quantum** **mechanics** as the complete and consistent physical theory which is compatible with all known experimental results. And also starting from the elegant conception of the de-coherence proposed in 1970 by D. Zeh, it is possible to explain that the various branches of the unique wave function, describing these worlds, are oscillating in time with phase shift and therefore each for other as if do not exist [15].

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A new framework in **quantum** chemistry has been proposed recently (“An approach to first principles electronic structure calculation by symbolic- numeric computation” by A. Kikuchi). It is based on the modern tech- nique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular or- bital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The inde- terminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Gr¨ obner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this arti- cle, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geom- etry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in **quantum** **mechanics**. We solve simple problems in “**quantum**

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I leave insisted on the difficulties presented by the non-localisation of the particle and the subjective character of the wave packet, e/ , in the contemporary interpretation, but thus [r]

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We can not only bring time operator in **quantum** **mechanics** (non-relativistic) but also determine its Eigen value, commutation relation of its square with energy and some of the properties of time operator like either it is Hermitian or not, either its expectation value is real or complex for a wave packet etc. Exactly these are what I have done.

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urement theory (with the interpretation (F)). And, for example, **quantum** **mechanics** can be fortu- nately described in this language. And moreover, almost all scientists have already mastered this language partially and informally since statistics (at least, its basic part) is characterized as one of as- pects of measurement theory (cf. [2-6]).

(GRW), Finkelstein’s **quantum** relativity, Noyes’s bit-string physics, Bastin and Kilmister’s combinatorial physics, Hiley’s process physics [8] [9]. Most of these have not gained much purchase within the larger physics community, possibly because the path back to standard **quantum** **mechanics** is not straightforward. The necessity to consider discrete models arises from considerations in **quantum** gravity [10], from the need to avoid diver- gences in **quantum** field theories, and from recent work by Gisin [11], who constructed a Bell type inequality showing that either one must reject the principle of continuity or accept instantaneous information transfer be- tween space-like separated entities (thus rejecting special relativity). In the model presented below, continuity is recovered via an interpolation procedure (based upon an idea of Kempf [12]) and **quantum** **mechanics** (at least non-relativistic **quantum** **mechanics**) arises directly as an effective theory when a continuum idealization can be assumed.

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Although the time-energy uncertainty relation is consistent with experiment, it is not derived from the non- commuting property of relative operators since there is no time operator in **quantum** theory. We think that this relation should be an intrinsic attribute for the time-energy space. When mentioned the space-time Feynman pointed out [23] : “We have discovered four quantities which transform like x , y , z , and t , and which we call the four-vector-momentum, …, it can be represented on a space-time diagram of a moving particle as an “arrow” tangent to the path. This is an arrow has a time component equal to the energy”. According Feynman, energy and time are dual to each other. At first, we get a dual relation for a cotangent basis dt and tangent ba- sis

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