The field of mirror symmetry has been a focal point in the last twenty years of in- teraction between geometry and physics. Mirror symmetry first started as a duality amongst two different (2,2) superconformal field theories (SCFT) and then provided a conjectural framework for two Calabi-Yau varieties M and **W** to interchange var- ious geometric and physical data. Consider a Calabi-Yau threefold M . When one looks at a local neighborhood of the Calabi-Yau moduli space near M , one views the moduli space as a product of the moduli space of complex structure M **c**-x (X)

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for the blending functions, of CAGD is high. There’re 13 desirable properties: 1. well-defined, 2. convex hull, 3. smooth, 4. interpolates end points, etc. For the whole list and descriptions of the 13 properties, see the paper for details. So we can see that to find suitable blending functions satisfying all of the 13 properties, even half of them, is not an easy job. Motivated by the observation that a function satisfying the properties should first be a discrete distribution function and the fact that Polya urn model is usually a good choice to construct discrete distributions, Goldman used the Polya distribution functions, **D** **i** **n** (**t**), i.e. the probability of draw- ing exactly **i** balls in the first **n** trials, as the blending function with δ/(**R** 0 + **B** 0 )

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Standard Model is well-performing under the three-generation, but in the wake of more physics, fourth-generation leptons and quarks are introduced. In this paper, We will be reviewing various constraints surrounding quarks and leptons of 4th Generation and tried to show the importance of quarks to understand the baryogenesis. We talked about, reviewed existing parameters and set the updated lower limits of **t**’ and **b**’ by analysis. And predicted an updated version of lower mass bounds quarks and leptons. It is also reviewed that fourth- generation leptons are primarily not possible because of disintegration of Higgs Boson and an interpretation has been setup. And in final, we talked about the Unified Standard Model.

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In the context of structure learning, the Bayesian network structure is often identified as the Bayesian network itself because learning the parameters can be done once the structure has been learned. However, another implicit reason, which is important for this paper, is that the Bayesian network structure conveys a model on its own, a conditional independence model. More concretely, as Whittaker (1990, pg. 207), we use the term model to specify an arbitrary family of probability distributions that satisfies a set of CI restrictions in the following way. A probability distribution P is Markov over a graph **G** if every CI restriction encoded in **G** is satisfied by P . A graphical Markov model (GMM), denoted by M(**G**), is the family of probability distributions that are Markov over **G** (Whittaker, 1990, pg. 13). One also says that **G** determines the GMM M(**G**).

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For the Asai **L**-function, we need an analogue of Lemma 6.1.4. But to the best of our knowledge, the complete analogue of Lemma 6.1.4 is not known. For our purpose, however, we have only to show non-vanishing of the Asai **L**-function at **s** = 1, 2 so that we can apply Theorem 1.0.1. Non-vanishing at **s** = 1 is done in [F1], which is also discussed in [Rb5, p.302]. Non-vanishing at **s** = 2 follows from absolute convergence of the Euler product which can be proven by an elementary argument as follows.

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Figure 9 shows the absorption versus the wavelength λ of a grid with a dielectric optimized for a wavelength of 100 µm. The parameters a and **g**, respectively, equal 3 µm and 20 µm. The absorption is optimized only for a band of frequency. This is partially because of the dielectric, which can reduce the absorption instead of to increase it, if it is used at frequencies different from those for which it was designed. In that case, absorbers have a finite bandwidth.

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In their attempt of understanding the relation between the local and global topo- logical structure of stratified spaces, Cappell and Shaneson ([4]) investigated the invariants associated with a stratified pseudomanifold X, PL-embedded in codimen- sion two in a manifold **Y** (e.g., X might be a hypersurface in a smooth algebraic variety). In describing the **L**-classes of the subspace X, they use as a main tool the peripheral complex **R** • , a torsion, self-dual, perverse sheaf, supported on X (here

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As we have seen in previous chapters, the Maritime Worker was placed at a particular historical, political and social juncture. It attempted to exploit the features that comprised this juncture into a socialist program of political and trade union development. These features were embodied in the text of the Maritime Worker in a number of ways, and are found in historical articles, articles of broad social commentary such as those which reflected on religion and class, political commentary and idiomatic political quotes, as well as articles of general interest. All these features of coherency and intelligibility combined against the backdrop of a particular historical circumstance in which the objectives of the Maritime Worker were clearly to make sense of the competing features of signification which abounded in this period. The task was then to try and direct them towards specific political and industrial outcomes for the Waterside Workers' Federation under the banner of a general socialist reorientation of society and its political systems. Therefore the ideological agenda which drove the Waterside Workers' Federation was one in which it was envisaged that the different discourses which made up the collective consciousness of Australian waterside workers could be subsumed into a comprehensive whole. The Maritime Worker was clearly designed for ideological purposes in the sense that it was believed that control of ideas and images could be used to bring about change and to create a sense of political identification for its readers. Healy stated this purpose in the inaugural edition of the Maritime Worker when he declared its function to be "an organising and propaganda m **e** **d** **i** **u** m " . **T** **h** **e** Maritime Worker therefore consisted of an amalgam of different discourses - some having their basis in Australian Labor Party traditions, others sourcing from the political texts of the Soviet Union and so forth. This notion of discourse is being used in its most general sense, in that what is being talked about is the social element of language - its content, function and social significance. This notion of discourse can be found also in ideology in which the concept relates, for instance, to those features by which institutions (university history faculties or unions) produce specific ways or modes of talking that are related to the place and nature of that institution. We can say therefore that discourse produces a set

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In our simulations, we used **N** = 16 standard cubic splines as was done in [1]. In order to produce trans- verse vibrations, the voltage spikes were negatives of each other and were triangular in shape. They had a dura- tion of 0.001 seconds with a maximum height of 100 V at **t** = 0.0005 seconds. Beam displacements were measured from **t** = 0 to **t** = 0.01 at 1000 time instances.

One can picture a Sieve as a bipartite graph with the cap above the base and the arrows pointing downward (e.g., Fig. 1). The containers are not con- strained by the type of point and arrow objects, so Sieve must be understood as a library of meta-objects and meta-algorithms (a template library in the **C**++ notation), which generates appropriate code upon instantiation of basis objects. We primarily have the **C**++ setting in mind, although appropriate Python and **C** bindings have been provided in our reference implementation. A Sieve can be made into a Map in two different ways, by identifying either cone or support with restrict. Each can be done with a simple adapter class and allows all the basic Map algorithms to be applied to Sieve objects as well as their descendants, such as Sieves.

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• Nagaveni. **N** received the B.Sc., M.Sc and B.Ed de- grees in Mathematics from Bharathiar University, India in 1985,1987 and 1988 respectively. M.Phil de- gree from Avinashilingam University, India in 1989 and M.Ed degree from Annamalai University, India in 1992. And Ph.D degree in the area of Topology in Mathematics from Bharathiar University, India in 2000. Since 1992, She has been with the department of Mathematics coimbatore Institute of Technology, Coimbatore Tamil Nadu, India where she is currently as Assistant Professor. She is engaged as a research supervisor and her research interests includes Topol- ogy, Fuzzy sets and continuous function, data min- ing, distributed computing, Web mining and privacy preservalign in data mining. She is the member in Indian Science congress Association (ICSA). she has been presented many research papers in the annual conference of ICSA. She has been published many papers in the international and national Journals. • Gangadharan SAI SUNDARA KRISHNAN received

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In addition, on macroscopic level it is sensible impose immiscibility condition (9), which is equivalent to (34). Whilst using this approximation, one can introduce ad- ditional microscopic dissipative term for regularization purposes (introducing energy dissipation on the diffusive interface). If one takes microscopic dynamics to be that of gradient flow (and introducing appropriate dissipation **D**), variation produces Allen- Cahn/Navier-Stokes system. While to get the phase field to satisfy conservation law, one can introduce “Darcy’s like” dissipation (proportional to relative drag) and deduce Cahn-Hilliard/Navier-Stokes system.

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elastic stress M , as a dependent variable, the system is closed in M and the well-known Oldroyd-**B** equations constitutive will be recovered, which has been extensively studied [52, 58, 59, 30, 86, 35]. In general, one may hope that the closure equations will help to solve or approximate f . However, since the energy law becomes inadequate to provide any closed system for M after this momentum closure procedure, the well-posedness of both the original problem and the closure problem are still not complete except for the local existence [7, 108]. In [85], the well-posedness of the dumbbell system in the near equilibrium situations was investigated.

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The automatic test data generation for programs with vari- able length of array with variable number of iterations using traditional path oriented method is very costly. Because the number of infeasible paths increase exponentially. Although the path prefix method solves this problem to some extent but it fails in terms of code coverage. we have got a mathematical relation between number of iterations and array size that can easily compute best **k** for maximum coverage.

where **S** could be of a two-surface with arbitrary topology. In the simplest prac- tical case, however, **S** would have either planar, cylindrical, toroidal or spherical topology. In these cases, we may assume that there exists a smooth real function ρ : Σ → **R** whose ρ = const level sets give the **S** ρ leaves of the foliation and that its

An intensity of response from KCl solution indicates the hydrodynamic explanation is at least insufficient. If our pro- posed hydrodynamic explanation were close to reality, then (ceteris paribus) the intensity would have been much less than one from NaCl solution because the dielectric friction coeffi- cients for **K** + and Cl – in water are very close to each other at the range of temperatures from +5°**C** up to +25°**C** 38,39 . For the further development of the hydrodynamic model one may find usefull some novel theoretical approaches capable of the unsteady fluid flow description at the microscopic level, for example, the so-called theories of complex fluids 40 .

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Thus, we start with a very steep downward sloping line going through (0, **r**) and rotate it anti-clockwise while we have an attainable portfolio. The ‘last’ portfolio is called the Optimum Portfolio of Risky Assets (OPRA). We will quantify it by observing that of all such lines going through the attainable region it is the one with maximal gradient. The investor can now place themselves anywhere on this line through an appropriate amount of lending or borrowing and using the remainder (which could be greater than one, if borrowing occurs - this is known as gearing) to buy the OPRA.

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