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Vashistha Vinod Kumar Kumar Anuj Das Dipak Kumar Alwera Shiv Vyas Renu Sharma Vivek Sethi Sonika Pullabhotla Rajasekhar Nagar Hariom 《平面色谱法杂志一现代薄层色谱法》2021,34(3):211-215
JPC – Journal of Planar Chromatography – Modern TLC - This work reports the enantioresolution of (RS)-acebutolol (ACB) by a thin-layer chromatographic method involving colistin sulfate... 相似文献
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In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation(product) in a particular region.The model exhibits two equilibria,namely,the adopter-free and an interior equilibrium.The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number(BIN) RA.It is investigated that the adopter free steady-state is stable if RA <1.By conside... 相似文献
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Anuj Dawar 《Annals of Pure and Applied Logic》2009,161(1):1-42
We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem’s theorem, which says that a first-order formula is invariant under bisimulation if, and only if, it is equivalent to a formula of basic modal logic. The present investigation primarily concerns ramifications for specific classes of structures. We study in particular model classes defined through conditions on the underlying frames, with a focus on frame classes that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics. Classical model theoretic arguments do not apply to many of the most interesting classes-for instance, rooted frames, finite rooted frames, finite transitive frames, well-founded transitive frames, finite equivalence frames-as these are not elementary. Instead we develop and extend the game-based analysis (first-order Ehrenfeucht-Fraïssé versus bisimulation games) over such classes and provide bisimulation preserving model constructions within these classes. Over most of the classes considered, we obtain finite model theory analogues of the classically expected characterisations, with new proofs also for the classical setting. The class of transitive frames is a notable exception, with a marked difference between the classical and the finite model theory of bisimulation invariant first-order properties. Over the class of all finite transitive frames in particular, we find that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic. We obtain ramifications of the de Jongh-Sambin theorem and a new and specific analogue of the Janin-Walukiewicz characterisation of bisimulation invariant monadic second-order for finite transitive frames. 相似文献
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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(11):3560-3565
It is well known that if are algebraic number fields with coprime discriminants, then the composite ring is integrally closed and are linearly disjoint over the field of rationals, being the ring of algebraic integers of . In an attempt to prove the converse of the above result, in this paper we prove that if are finite separable extensions of a valued field of arbitrary rank which are linearly disjoint over and if the integral closure of the valuation ring of v in is a free -module for with integrally closed, then the discriminant of either or of is the unit ideal. We quickly deduce from this result that for algebraic number fields linearly disjoint over for which is integrally closed, the relative discriminants of and must be coprime. 相似文献
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In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage(time delay) is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period(time delay, τ) passes through a critical value. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included. 相似文献
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Anuj Dawar Kees Doets Steven Lindell Scott Weinstein 《Mathematical Logic Quarterly》1998,44(3):349-353
This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO(<, BIT) = FO(BIT). 相似文献