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A significant focal idea presented in [2-3], is that of neat reducts. In this paper, we apply neat reducts on some classes of algebras like cylindric algebras, quasi-polyadic algebras and quasi-polyadic equality algebras. [ABSTRACT FROM AUTHOR]

Let \(2

Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let \(\mathbf{PA}_{\alpha}(\mathsf{PEA}_{\alpha})\) stand for the class of polyadic (equality) algebras of dimension \(\alpha\). We reprove that the class \(\mathsf{CRCA}_n\) of completely representable \(\mathsf{CA}_n\)s, and the class \(\sf CRRA\) of completely representable \(\mathsf{RA}\)s are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety \(\sf V\) between polyadic algebras of dimension \(n\) and diagonal free \(\mathsf{CA}_n\)s. We show that that the class of completely and strongly representable algebras in \(\sf V\) is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class \(\sf CRRA\) is not closed under \(\equiv_{\infty,\omega}\). In contrast, we show that given \(\alpha\geq \omega\), and an atomic \(\mathfrak{A}\in \mathsf{PEA}_{\alpha}\), then for any \(n

Let 2 < n < ω. Then CAn denotes the class of cylindric algebras of dimension n, RCAn denotes the class of representable CAns, CRCAn denotes the class of completely representable CAns, and NrnCAω(⊆ CAn) denotes the class of n-neat reducts of CAωs. The elementary closure of the class CRCAns (Kn) and the nonelementary class At(NrnCAω) are characterized using two-player zero-sum games, where At is the operator of forming atom structures. It is shown that Kn is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of ScNrnCAω where Sc is the operation of forming complete subalgebras. For any class L such that AtNrnCAω ⊆ L ⊆ AtKn, it is proved that SPCmL = RCAn, where Cm is the dual operator to At; that of forming complex algebras. It is also shown that any class K between CRCAn ∩ SdNrnCAω and ScNrnCAn+3 is not first order definable, where Sd is the operation of forming dense subalgebras, and that for any 2 < n < m, any l ≥ n + 3 any any class K such that At(NrnCAm ∩ CRCAn) ⊆ K ⊆ AtScNrnCAl, K is not not first order definable either. [ABSTRACT FROM AUTHOR]

Fix a finite ordinal n ≥ 3 and let α be an arbitrary ordinal. Let CAn denote the class of cylindric algebras of dimension n and RA denote the class of relation algebras. Let PAα(PEAα) stand for the class of polyadic (equality) algebras of dimension α. We reprove that the class CRCAn of completely representable CAns, and the class CRRA of completely representable RAs are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety V between polyadic algebras of dimension n and diagonal free CAns. We show that that the class of completely and strongly representable algebras in V is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class CRRA is not closed under =1,ω. In contrast, we show that given α ≥ ω, and an atomic A 2 PEAα, then for any n < !, NrnA is a completely representable PEAn. We show that for any α ≥ ω, the class of completely representable algebras in certain reducts of PAαs, that happen to be varieties, is elementary. We show that for α ≥ ω, the the class of polyadic-cylindric algebras dimension α, introduced by Ferenczi, the completely representable algebras (slightly altering representing algebras) coincide with the atomic ones. In the last algebras cylindrifications commute only one way, in a sense weaker than full fledged commutativity of cylindrifications enjoyed by classical cylindric and polyadic algebras. Finally, we address closure under Dedekind-MacNeille completions for cylindric-like algebras of dimension n and PAαs for α an infinite ordinal, proving negative results for the first and positive ones for the second. [ABSTRACT FROM AUTHOR]

Let α be an ordinal and L be a unimodal logic (like S4 or S5). A modal cylindric algebra of dimension α, an LCAα, is a cylindric algebra of dimension α, expanded with α-many L modalities. For a frame (U, R) of L, each k < α, one defines a diamond box operator on. This defines the semantics of the L modalities in set algebras, with the rest of the operations defined like in cylindric set algebras of dimension α. We study interpolation properties for the corresponding predicate logic having α-many variables. Our results are valid for any reflexive L whose frames contain the universal frames (U, U × U). In particular, they hold for K5CAα, S4CAα (which is an algebraizable extension of topological predicate logic with semantics induced by Alexandrov topologies). [ABSTRACT FROM AUTHOR]

Fix 2 < n < ω and let CAn denote the class of cyindric algebras of dimension n. Roughly CAn is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by Ln. The variety RCAn of representable CAns reflects algebraically the semantics of Ln. Members of RCAn are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CAn has a finite equational axiomatization, RCAn is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CAn substantially richer than that of Boolean algebras, just as much as Lω,ω is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCAn are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever 𝔄 ∈ V is atomic, then its Dedekind-MacNeille completion, sometimes referred to as its minimal completion, is also in V. From our hitherto obtained algebraic results we show, employing the powerful machinery of algebraic logic, that the celebrated Henkin-Orey omitting types theorem, which is one of the classical first (historically) cornerstones of model theory of Lω,ω, fails dramatically for Ln even if we allow certain generalized models that are only locallly clasfsical. It is also shown that any class K such that N r n C A ω ∩ CRC A n ⊆ ¯ K ⊆ ¯ S c N r n C A n + 3 , where CRCAn is the class of completely representable CAns, and Sc denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that S d RaC A ω ⊆ ¯ K ⊆ ¯ S c RaC A 5 is not elementary, where Sd denotes the operation of forming dense subalgebra. [ABSTRACT FROM AUTHOR]

We have considered a homogeneously aligned liquid crystal (HALC) microvolume confined between two infinitely long horizontal coaxial cylinders and investigated dynamic field pumping, i.e., studied the interactions between director, velocity, and electric E fields as well as a radially applied temperature gradient ∇T, where the inner cylinder is kept at a lower temperature than the outer one. In order to elucidate the role of ∇T in producing hydrodynamic flow u, we have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HALC cavity. Calculations show that only under the influence of ∇T does the initially quiescent HALC sample settle down to a stationary flow regime with horizontal component of velocity ueq(r). The effects of ∇T and of the size of the HALC cavity on magnitude and direction of ueq(r) have been investigated for a number of hydrodynamic regimes. Calculations also showed that E influences only the director redistribution across the HALC but not the magnitude of the velocity ueq(r). [ABSTRACT FROM AUTHOR]

This paper proposes a new tool path generation method for machining impellers with five-axis machines. Using the geometric characteristics of impellers, the proposed method first computes the tool path in the cylindrical coordinates and then converts it into the cartesian coordinates. The proposed method is simpler, more efficient, and requires less user interactions than known methods. Collision avoidance and optimum cutting condition issues are also addressed in this paper. [ABSTRACT FROM AUTHOR]

In this work, a qualitative and quantitative characterization of the three-dimensional flow in a lid-driven cylindrical cavity with different optical techniques is presented. Mach–Zehnder interferometry and photographic techniques have been used for a qualitative description of some flow features. However, the real challenge is to obtain quantitative measurements, as the cavity dimensions and geometry prevent the application of 3D digital techniques for measuring the flow velocity in the whole cavity with enough spatial resolution. Digital in-line holography was applied to the measure of the vortex-breakdown bubble that appears near the cavity bottom at Re = 2000. A 22 × 22 × 80 mm3 volume was recorded, its longest dimension parallel to the camera optical axis. This large volume in a liquid fluid combined with a high particle density forces us to develop new analysis strategies. Holograms have been analyzed using a new method, called Adaptive Cross Correlation with Tracking From Beginning, which includes the use of the reconstructed complex amplitude for particle localization. Particle tracking is based on the three-dimensional cross correlation of three-dimensional interrogation windows. The particle set defined in the first hologram is always used to find the particle position in subsequent holograms. This method provides an accurate 3D velocity map and the vortex-breakdown bubble spatial structure. Experimental and numerical data show a very good agreement. A new criterion for determining the accuracy in the particle position along the optical axis is introduced, achieving a spatial resolution of 0.1 mm. This tracking method can be applied not only to laminar flows but also to turbulent flows. [ABSTRACT FROM AUTHOR]

In this paper, we give new proofs of the celebrated Andréka-Resek-Thompson representability results of certain axiomatized cylindric-like algebras. Such representability results provide completeness theorems for variants of first order logic, that can also be viewed as multi-modal logics. The proofs herein are combinatorial and we also use some techniques from game theory. [ABSTRACT FROM AUTHOR]

For β an ordinal, let PEAβ (SetPEAβ) denote the class of polyadic equality (set) algebras of dimension β. We show that for any infinite ordinal α, if A ∈ PEA α is atomic, then for any n < ω, the n-neat reduct of A , in symbols ℜ r n A → B , is a completely representable PEAn (regardless of the representability of A). That is to say, for all non-zero a ∈ ℜ r n A , there is a B a ∈ SetPEA n and a homomorphism f a : ℜ r n A → B such that fa(a) ≠ 0 and f a (∑ X) = ∪ x ∈ X f a (x) for any X ⊂ = A for which ∑ X exists. We give new proofs that various classes consisting solely of completely representable algebras of relations are not elementary; we further show that the class of completely representable relation algebras is not closed under ≡∞,ω. Various notions of representability (such as 'satisfying the Lyndon conditions', weak and strong) are lifted from the level of atom structures to that of atomic algebras and are further characterized via special neat embeddings. As a sample, we show that the class of atomic CAns satisfying the Lyndon conditions coincides with the class of atomic algebras in ElScNrnCAω, where El denotes 'elementary closure' and Sc is the operation of forming complete subalgebras. [ABSTRACT FROM AUTHOR]

This essay is about how the notion of "structure" in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic. [ABSTRACT FROM AUTHOR]

We consider a problem of calculus of variations motivated by the model of a tank filled with a given volume of liquid and draining through a small orifice according to Torricelli's law. We prove that given any length of time, some tank exists which drains in this time. Our main interest in this optimization (i.e., minimization and maximization) problem is that the usual Euler--Lagrange equation may not be used here, at least directly. We consider optimization for some similar physical models where Torricelli's law has to be modified. We also study optimization problems on the star graphs that are inspired by our physical model. [ABSTRACT FROM AUTHOR]

Abstract In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell lifting (that is, stack construction) technique. For the proof of the method's validity Lazard introduced a new notion of valuation of a multivariate polynomial at a point. However a gap in one of the key supporting results for his proof was subsequently noticed. In the present paper we provide a complete validity proof of Lazard's method. Our proof is based on the classical parametrized version of Puiseux's theorem and basic properties of Lazard's valuation. This result is significant because Lazard's method can be applied to any finite family of polynomials, without any assumption on the system of coordinates. It therefore has wider applicability and may be more efficient than other projection and lifting schemes for CAD. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce a new class of bargraphs – circular bargraphs , which are self-avoiding walks in a cylindrical lattice, and study the enumerations of them with respect to perimeter statistic. More precisely, we study the perimeter of a circular bargraph , a statistic defined naturally as the number of edges in the boundary of the bargraph. We also find an explicit formula for the total length of the perimeter over all bargraphs with n -cells. [ABSTRACT FROM AUTHOR]

Abstract In this paper, spectral methods based on conformal mappings are proposed to solve the Steklov eigenvalue problem and its related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain via conformal mappings. The eigenfunctions are expanded in Fourier series so the discretization leads to an eigenvalue problem for coefficients of Fourier series. For shape optimization problem, we use a gradient ascent approach to find the optimal domain which maximizes k th Steklov eigenvalue with a fixed area for a given k. The coefficients of Fourier series of mapping functions from a unit circle to optimal domains are obtained for several different k. [ABSTRACT FROM AUTHOR]

Highlights • Detailed numerical and experimental study of a full-scale condensing gas boiler. • Identified high emission regions due to locally varying burnt temperature levels. • CO emissions are caused by a freeze of CO oxidation due to a steep cooling gradient. • Majority of NO is formed within the flame front and not in post flame region. Abstract The condensing gas boiler technology has received increasing attention due to its very high efficiency of more than 90%, which is an increase of more than 15% compared to non-condensing boiler devices. With this, condensing gas boilers offer the chance to decrease the energy consumption and CO 2 emissions for domestic hot water and heating. While further increasing the energy efficiency of condensing boiler devices, pollutant emissions have to be considered as well since they are a threat to human health and therefore subject to continuously intensified governmental restrictions. In this study, a comprehensive investigation of the full-scale heating unit of a commercial condensing gas boiler was performed. Local measurements at different axial positions revealed an inhomogeneous distribution of CO and NO emissions due to varying temperature levels in the burnt region. Resolved simulations with finite rate chemistry identified a quenching of the CO oxidation reactions due to a fast depletion of OH radicals. Consequently, the CO concentration in the cooled exhaust gas is significantly higher than expected from chemical equilibrium calculations. Regarding NO formation, the majority of NO is found to be produced within the flame front, while only a small part is formed in the postflame region. A detailed pathway analysis pointed out that besides the well known thermal NO pathway, the NNH pathway has the highest contribution to the overall NO emissions. These insights open up possibilities to develop new condensing boiler generations where emission levels below the permitted limits can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, the potential application of the high-level canonical piecewise-linear model in the field of three-dimensional visualization is proposed. This idea emerges from the premise that a three-dimensional surface can be modeled by a continuous two-dimensional function. In this regard, the main contribution consists in providing a methodology for the construction of such function. For this purpose, the well-known algorithm used in the high-level canonical piecewise-linear model has been modified to achieve functions with greater graphing capability. One of the most notorious changes made with respect to the traditional methodology is the use of a new scheme of function domain partition. Contrary to the simplicial partitioning, in our proposal, an equally distributed angular partitioning is considered. With this, the resulting approximate function is expressed in cylindrical coordinates which overcome the typical limitation of graphs in Cartesian coordinates of only representing single-valued surfaces. Another remarkable change can be found in the range of evaluation of the function. Instead of using an open interval, in our approach, a closed interval from 0 to 2π is adopted. To support this proposal, illustrative case studies are reported. Numerical simulations demonstrate the effectiveness of this type of representation model not only in visual perception of three-dimensional surfaces, but also in more complex tasks like volume estimation. [ABSTRACT FROM AUTHOR]

Cylindrical detonations propagating in free space characterized by different activation energies were computationally studied. It is found that unstable detonations with the 2-D cellular structure have more velocity deficit than those without the cellular structure computed with the 1-D simulation. The weakening is due to lengthening of the detonation structure and the unreacted pocket behind the cylindrical front, while propagation sustenance depends strongly on the re-amplification and regeneration of transverse shocks and triple points. For low activation energies, cellular detonation can be initiated in free space through the subcritical initiation path due to absence of unreacted pockets, and the propagation is not very sensitive to the attenuation of transverse waves and triple points. However, for high activation energy the unreacted pocket aggravates initiation such that even a cellular detonation first established is prone to quench due to the lack of re-amplification of the transverse wave and the triple point. When considering confinement, it is demonstrated that a detonation that quenches in free space can be reinitiated in confined space. [ABSTRACT FROM AUTHOR]

In this paper, we analyse Mickens’ type non-standard finite difference schemes (NSFD) and establish their convergence. We then apply these schemes on Lane Emden equations. The numerical results thus obtained are compared with existing analytical solutions or with solutions computed with standard finite difference (FD) schemes. NSFD and FD solutions and their errors have also been compared graphically and observed that the errors in NSFD tends to zero as step size tends to zero. The result shows that the NSFD behave qualitatively in the same way as the original equations. NSFD approximate solution near singular point efficiently where FD fails to do so (Buckmire in Numer Methods Partial Differ Equ 19:380-398, 2003). [ABSTRACT FROM AUTHOR]

Inspired by the works of Dewar, Murty and Kotěšovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylindric partitions. We prove that the order of the asymptotic formula for the number of skew plane partitions of fixed width depends only on the width of the region, not on the profile (the skew zone) itself, while this is not true for cylindric partitions. [ABSTRACT FROM AUTHOR]

Cylindric algebras, or concept algebras as another name, form an interface between algebra, geometry and logic; they were invented by Alfred Tarski around 1947. We prove that there are 2|α| many varieties of geometric (i.e., representable) α-dimensional cylindric algebras, which means that 2|α| properties of definable relations of (possibly infinitary) models of first order theories can be expressed by formula schemes using α variables, where α is infinite. This solves Problem 4.2 in the 1985 Henkin-Monk-Tarski monograph [Cylindric algebras. Part II, Studies in Logic and the Foundations of Mathematics, vol. 115, North-Holland, Amsterdam, 1985]; the problem is restated by Németi [On varieties of cylindric algebras with applications to logic, Ann. Pure Appl. Logic 36 (1987), no. 3, 235-277] and Andréka, Monk, and Németi [Algebraic logic, Colloq. Math. Soc. János Bolyai, Vol. 54, North-Holland, Amsterdam, 1991]. For solving this problem, we devise a new construction, which we then use to solve Problem 2.13 of the 1971 Henkin-Monk-Tarski monograph [Cylindric algebras. Part I, Studies in Logic and the Foundations of Mathematics, vol. 64, North-Holland, Amsterdam, 1971] which concerns the structural description of geometric cylindric algebras. There are fewer varieties generated by locally finite-dimensional cylindric algebras, and we get a characterization of these among all the 2|α| varieties. As a by-product, we get a simple recursive enumeration of all the equations true of geometric cylindric algebras, and this can serve as a solution to Problem 4.1 of the 1985 Henkin-Monk-Tarski mono- graph. All of this has logical content and implications concerning ordinary first order logic with a countable number of variables. [ABSTRACT FROM AUTHOR]

In this article we discuss a method for constructing trace formulae for the heat-volume potential of the time-fractional diffusion equation to lateral surfaces of cylindrical domains and use these conditions to construct as well as to study a nonlocal initial boundary value problem for the time-fractional diffusion equation. [ABSTRACT FROM AUTHOR]

Using a linear stability analysis and the transfer matrix method, we investigate the surface instability of an imperfectly bonded multi-layered curved film interacting with a curved rigid contactor, another imperfectly bonded multi-layered curved film or an imperfectly bonded multi-layered simply-supported cylindrical shell in each case through the action of attractive van derWaals forces. The imperfect interface is modelled as a linear spring layer with vanishing thickness characterized by normal and tangential imperfect interface parameters. Detailed numerical results are presented to demonstrate the resulting analytical solutions. [ABSTRACT FROM AUTHOR]

The classes of non-commutative cylindric algebras and weakened cylindric algebras were shown, by Istv'an N'emeti, to have decidable equational theories. In this article, we give new proof for this result and we give an answer to the open problem, posed by N'emetin 1985, addressing the atomicity of the finitely generated free algebras of these classes. We prove that the free algebras of these classes are not atomic. [ABSTRACT FROM AUTHOR]

In this paper, we shall be concerned with interior controllability for a one-dimensional wave equation in a domain with moving boundary. When the speed of the moving endpoint is less than a certain constant which is less than the characteristic speed, we obtain exact controllability for this equation. [ABSTRACT FROM AUTHOR]

Sand-foam mixtures have many potential applications in the field of mining and construction. This paper conducts laboratory experiments to investigate rheological characteristics of sand-foam mixtures using free slump flow tests with a cylindrical geometry. It is expected that slump test can provide accurate results to identify the effects of sand concentration, foam:water ratio, and particle size on the rheology of sand-foam mixtures. Three distinct stages are observed in slump of sand foam mixtures. The effect foam:water ratio is more pronounced in variations of slump heights and diameters with time. Yield stress of sand foam mixtures are estimated using the slump model for cylindrical geometries. Estimated yield stress is overall in good agreement with the rheological measurements. Effect of particle size on yield stress of sand foam mixtures is found to be negligible except for dense mixtures (co > 0.6) with higher foam:water ratio (Gf = 0.3). The averaged bed shear stresses of mixtures are calculated using a simplified one-dimensional momentum equation. A comparison between the averaged bed shear stress and the yield stress of mixtures indicates two distinct behaviours of fluidlike and solidlike during the slump flow spread. Energy dissipation is estimated during the tests. The energy dissipation rates of light sand-foam mixtures are higher than those of dense mixtures. The total energy dissipation of sand-foam mixtures is approximately 95%, which is 10% higher than the energy dissipation of granular flow. [ABSTRACT FROM AUTHOR]

Two-phase flow is the simplest case of multiphase flow in which two phases are present for a pure component. The mini channel is considered as diameter below 3.0-0.2 mm and conventional channel is considered diameter above 3.0 mm. An experiment was conducted to study the adiabatic two-phase flow patterns in the circular test section with inner diameter of 1.1, 1.63, 2.0, 2.43 and 3.0 mm for horizontal orientation using air and water as a fluid. Different types of flow patterns found in the experiment. The parameters that affect most of these patterns and their transitions are channel size, phase superficial velocities (air and liquid) and surface tension. The superficial velocity of liquid and gas ranges from 0.01 to 66.70 and 0.01 to 3 m/s respectively. Two-phase flow pattern photos were recorded using a high speed CMOS camera. In this experiment different flow patterns were identified for different tube diameters that confirm the diameter effect on flow patterns in two-phase flows. Stratified flow was not observed for tube diameters less than 3.0 mm. Similarly, wavy-annular flow pattern was not observed in 1.6 and 1.0 mm diameter tubes due to the surface-tension effect and decrease in tube diameter. Buoyancy effects were clearly visible in 2.43 and 3.0 mm diameter tubes flow pattern. It has also observed that as the test-section diameter decreases the transition lines shift towards the higher gas and liquid velocity. However, the result of flow pattern lines in the present study has good agreement with the some of the existing flow patterns maps. [ABSTRACT FROM AUTHOR]

In this paper, we establish exact solutions of the Cauchy problem for the 3D cylindrically symmetric incompressible Navier-Stokes equations and further study the global existence and asymptotic behavior of solutions. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the first half of this article, we define a new weight homology functor on Voevodsky's category of effective motives and investigate some of its properties. In special cases, we recover Gillet-Soulé's weight homology and Geisser's Kato-Suslin homology. In the second half, we consider the notions of "co-étale" and "reduced" motives, and use the notions to a prove a theorem comparing motivic homology to étale motivic homology. Due to [19] we do not have to restrict to smooth schemes. [ABSTRACT FROM AUTHOR]

We present three equivalent definitions of S¹-equivariant symplectic homology. We show that, using rational coefficients, the positive part of S¹-equivariant symplectic homology is isomorphic to linearized contact homology when the latter is defined. We present several computations and applications, and introduce a substitute for cylindrical/linearized contact homology based on an S¹-equivariant construction. [ABSTRACT FROM AUTHOR]

The design and calibration of three simple flumes for flow measurements in open channels are discussed. The flumes are designed based on principles of critical flow in open channels. Critical flow is created through the contraction of the flow cross section by installing vertical cylindrical columns in an open channel. Calibrated equations are developed for each of the three flumes by combining the Pi Theorem principle with laboratory scale physical models. The three flumes are designed for application in prismatic (trapezoidal, rectangular, and circular) channels. The calibrated equations can be used for design and calibration of the flumes regardless of the flumes or channel dimensions. The equations are validated using field scale flumes, and a design example is provided for free flow conditions. [ABSTRACT FROM AUTHOR]

We obtain asymptotic formulas uniform with respect to the index p > 0 for the Hankel functions H( z) ( j = 1, 2) for large | z| in the complex domain. These formulas generalize those known for the real argument. [ABSTRACT FROM AUTHOR]

In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P2n and P3n, which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0-P3n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of threedimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles. [ABSTRACT FROM AUTHOR]

The paper presents the cylindrical shape detailed study, frequently used in industrial design. The geometrical cylindric shape is the ideal (perfect) shape which is given by mathematical equation. The functional shape is the ultimate (final) shape which is obtained using different technological proceedings and it is a part of designed device. Also, the paper presents geometrical shapes with variable geometry, shapes obtained wrapping small thickeness iron sheets, or products obtained arranging different cylindrical shapes. [ABSTRACT FROM AUTHOR]

This paper aims to develop a generic framework for detecting contact between cylindrical particles in discrete element modelling based on a full exploitation of the axi-symmetrical property of cylinders. The main contributions include: (1) A four-parameter based local representative system is derived to describe the spatial relationship between two cylinders so that the 3D cylinder–cylinder intersection problem can be reduced to a series of 2D circle–ellipse intersections, which considerably simplifies the contact detection procedure. (2) A two-stage contact detection scheme is proposed in which no-overlap contact pairs are identified in the first overlap check stage, and then the actual overlap region is determined in the second resolution stage and represented by two schemes: the layered representation which is generic, and the edge representation which is numerically more efficient but less accurate. (3) The most significant contribution is the development of two theorems that establish a fundamental relationship between the contact point and contact normal of two contacting cylinders, offering a simple approach to determining the normal direction based on the contact point and vice versa. These theorems are valid not only for cylinders, but also for any axi-symmetrical shapes and their combinations. Some numerical issues are discussed. Numerical examples are presented to illustrate the capability and applicability of the proposed methodologies. [ABSTRACT FROM AUTHOR]

We consider an instanton, A, with L -bounded curvature F on the cylindrical manifold $${Z=\mathbf{R} \times M}$$ , where M is a closed Riemannian n-manifold, $${n \geq 4}$$ . We assume M admits a smooth 3-form P and a smooth 4-form Q satisfy $${dP=4Q}$$ and $${d\ast_{M}{Q}=(n-3)\ast_{M}P}$$ . Manifolds with these forms include nearly Kähler 6-manifolds and nearly parallel G -manifolds in dimension 7. Then we can prove that the instanton must be a flat connection. [ABSTRACT FROM AUTHOR]

We prove a criterion for pointwise stabilization of bounded solutions to nonlinear parabolic p-Laplacian type equations in a cylindrical domain with an unbounded base. The criterion is formulated in terms of a Wiener series or integral and can be regarded as the condition of regularity of a point at infinity. Bibliography: 32 titles. [ABSTRACT FROM AUTHOR]