Search

We consider a single server discrete-time system with a fixed number of users where the server picks operating points from a compact, convex, and coordinate convex set. For this system, [...]

The design of a quasi-null lens system for the fabrication of an aspheric oblate convex ellipsoidal mirror is presented. The Performance and tolerance of the system have been analyzed. The system has been applied successfully for the fabrication of the primary mirror of the Wide Angle Camera (WAC), the imaging system onboard the Rosetta, the European Space Agency cornerstone mission dedicated to the exploration of a comet. The WAC is based on an off-axis two-mirror configuration, in which the primary mirror is an oblate convex ellipsoid with a significant conic constant. OCIS codes: 350.1260, 220.1000, 120.4610.

Byline: V. V. Makeev (1) Abstract: Existence theorems are proved for collections of affine diameters of a convex body that satisfy various additional conditions. The area of a convex planar figure is estimated via the maximal length of a chord dividing the area of the figure in a given ratio. Bibliography: 7 titles. Author Affiliation: (1) St.Petersburg State University, St. Petersburg, Russia Article History: Registration Date: 05/10/2005 Received Date: 25/12/2001 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 252--261.

An experimental investigation was conducted to study the transonic flow past convex corners. The mean surface pressure indicated strong--viscous interactions, and the interaction region increased with the freestream Mach number and the convex-corner angle. Unsteadiness of the interaction was characterized by an intermittent region and a local peak pressure fluctuation. The peak pressure fluctuations and the tentative boundary between the attached and separated flows could be scaled with the convex-corner angle and a second-order freestream Mach number ([M.sup.2.sub.[infinity]][eta]).

Abstract: Several combinatorial geometry properties of convex compact sets are proved by topological methods. It is proved that if K .sub.1,... ,K .sub.n-1 are convex compacta in R.sup.n , then there is an (n-2)-plane E.sup.n such that for each i=1,2,... ,n-1 there exist three (two orthogonal) hyperplanes containing E and dividing .sub.Ki into six (four) parts of equal volume. It is also proved that for every two bounded continuous distributions of masses in R.sup.3 centrally symmetric with respect to the origin there are three planes dividing both masses into eight equal parts. Bibliography: 9 titles. Article History: Registration Date: 20/10/2004

Abstract: Let Q.sup.3 be a compact convex body such that for each parallel projection onto any plane no two opposite faces of Q are projected strictly inside the projection of the entire Q. Then Q is either a cone, or a frustum of a trihedral pyramid, or a prism (possibly with nonparallel bases). Bibliography: 1 title. Article History: Registration Date: 20/10/2004

Abstract: It is shown that the set [G,[]].sub.I of immersed linear networks in R.sup.n that are parallel to a given immersed linear network [GAMMA] :G.sup.n and have the same boundary [] as I is a convex polyhedral subset of the configuration space of movable vertices of the graph G. The dimension of [G,[]].sub.I is calculated, and the number of its maximal faces is estimated. As an application, the spaces of all locally minimal and weighted minimal networks with fixed boundary and topology in R.sup.n are described. Bibliography: 21 titles. Article History: Registration Date: 20/10/2004

Abstract: There is a k-gon of minimal area containing a given convex n-gon (k&lt n) such that k-1 sides of the n-gon lie on the sides of the k-gon. All midpoints of the sides of the k-gon belong to the n-gon. Bibliography: 3 titles. Article History: Registration Date: 20/10/2004

Abstract: Let K be a family of translations of a convex compact set K.sup.2 such that every two elements of K have a common point. Then there exist three points a.sub.1 ,\ a.sub.2 ,\ a.sub.3.sup.2 such that each element of K contains one of these points. This answers in the affirmative an old question by Grunbaum. Bibliography: 13 titles. Article History: Registration Date: 20/10/2004

Byline: V. A. Zalgaller (1), O. M. Merkulova (2) Abstract: An analog of the Apollonian circle on the Lobachevski plane is a convex analytic curve. A similar curve on the sphere may be nonconvex and may contain one singular (nonanalytic) point. It follows that there may exist more than one spherical belt separating two given compacta on the sphere and having the maximum possible ratio of the exterior and interior radii. Bibliography: 3 titles. Author Affiliation: (1) St.Petersburg Department of the Steklov Mathematical Institute, Russia (2) St.Petersburg State University, Russia Article History: Registration Date: 25/10/2004

Byline: V. A. Zalgaller (1) Abstract: Let K.sub.0 ,K.sub.1 ,...,K.sub.m be nonempty convex bodies in R.sup.n . Let r.sub.1 ,...,r.sub.m be vectors in R.sup.n , let [rho] = (r.sub.1 ,...,r.sub.m ).sup.nm , and let K.sub.0[intersection][intersection] .sub.i = 1.sup.m (K.sub.i + r.sub.i ) . Then D =\[rho]|[PHI].([rho] )\.sup.nm is a convex set, and the family of sets \[rho]|[PHI].([rho] )\ .sub.[rho][member of] D is concave. Let .sub.[rho][PHI] ([rho] ) = k 1 . Then for the mean cross-sectional measures W_v (\Phi (\rho )), [nu] = 0,1,...,k - 1 , the functions [nu] = 0,1,...,k - 1\\ [square root of (term)][k -[nu] ]W.sub.[nu] ([PHI] ([rho] )) = k\\ are concave on D. (Note that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGxbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiabfA6agjaacIcacqaH% bpGCcaGGPaGaaiykaiabg2da9iaabAfacaqGVbGaaeiBamaaBaaale% aatCvAUfKttLearyqr1ngBPrgaiuGacqWFRbWAaeqaaOGaeuOPdyKa% aiikaiabeg8aYjaacMcaaaa!4EE7!\[W_0 (\Phi (\rho )) = {\text{Vol}}_k\Phi (\rho )\] is the k-volume.) Bibliography: 2 titles. Author Affiliation: (1) St.Petersburg Department of the Steklov Mathematical Institute, Russia Article History: Registration Date: 25/10/2004

Computations have been conducted on curved, three-dimensional discrete-hole film cooling geometries that included the mainflow, injection hole, and supply plenum regions. Both convex and concave film cooling geometries were studied. The effects of several film cooling parameters have been investigated, including the effects of blowing ratio, injection angle, hole length, hole spacing, and hole staggering. The blowing ratio was varied from 0.5 to 1.5, the injection angle from 35 to 65 deg, the hole length from 1.75D to 6.0D, and the hole spacing from 2D to 3D. The staggered-hole arrangement considered included two rows. The computations were performed by solving the fully elliptic, three-dimensional Navier-Stokes equations over a body-fitted grid. Turbulence closure was achieved using a modified k-(epsilon) model in which algebraic relations were used for the turbulent viscosity and the turbulent Prandtl number. The results presented and discussed include plots of adiabatic effectiveness as well as plots of velocity contours and velocity vectors in cross-stream planes. The present study reveals that the blowing ratio, hole spacing, and hole staggering are among the most significant film cooling parameters. Furthermore: (1) The optimum blowing ratios for curved surfaces are higher than those for fiat surfaces, (2) a reduction of hole spacing from 3D to 2D resulted in a very significant increase in adiabatic effectiveness, especially on the concave surface, (3) the increase in cooling effectiveness with decreasing hole spacing was found to be due to not only the increased coolant mass per unit area, but also the smaller jet penetration and the weaker counterrotating vortices, (4)for all practical purposes, the hole length was found to be a much less significant film cooling parameter.

The influence of convex curvature on the mean and turbulent characteristics of three-dimensional wall jet generated from a circular orifice geometry is reported in this paper. Mild, moderate, and strong curvature are considered. Detailed results on a plane surface are also obtained for comparison purposes. Among the mean properties, the decay rate of maximum velocity and the growth of length scales are significantly altered due to curvature effects. The turbulent components, both turbulent normal and shear stresses, show an increase with curvature parameter in a direction normal to the curved surfaces; however, there is very little change in the spanwise direction.

Incremental length diffraction coefficients (ILDC's) are obtained for the shadow boundaries of perfectly electrically conducting (PEC) convex cylinders of general cross section. A two-step procedure is used. First, the nonuniform (NU) current in the vicinity of the shadow boundary is approximated using Fock functions. The product of the approximated current and the free-space Green's function is then integrated on a differential strip of the cylinder surface transverse to the shadow boundary to obtain the ILDC's. This integration is performed in closed form by employing quadratic polynomial approximations for the amplitude and unwrapped phase of the integrand. Examples are given of both the current approximations and the integration procedure. Finally, as an example, the scattered far field of a PEC sphere is obtained by adding the integral of the NU ILDC's of a circular cylinder along the shadow boundary of the sphere to the physical optics (PO) far field of the sphere. This correction to the PO field is shown to significantly improve upon the accuracy of the PO far-field approximation to the total scattered field of the sphere. Index Terms - Physical theory of diffraction.

An algorithm splits the polygon into two congruent pieces by using a successful cut. The set of all endpoints of the bordering line segments of the polygon is split by constructing two paths that travel in parallel. The algorithm also leads to a theorem on splitting convex shapes. The theorem states that a convex polygon can be split in two properly congruent pieces if it has rotational symmetry. Three splittable polygons are presented as an exercise.

This paper describes an algorithm that robustly locates salient convex collections of line segments in an image. The algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. We give an expected case analysis of the algorithm's performance. This demonstrates that salient convexity is unlikely to occur at random, and hence is a strong clue that grouped line segments reflect underlying structure in the scene. We also show that our algorithm's run time is O([n.sup.2]log(n) + nm), when we wish to find the m most salient groups in an image with n line segments. We support this analysis with experiments on real data, and demonstrate the grouping system as part of a complete recognition system. Index Terms - Grouping, perceptual organization, convexity, proximity, nonaccidental properties, robust, efficiency, recognition.

Various refractive null-testing arrangements have been used over the years for testing concave nonspherical mirrors. This paper presents a method for null testing that uses a single plano-convex lens to compensate for the spherical aberration of a concave conic mirror when tested at its center of curvature. This testing method, called the Ross null test, requires a high-quality null lens and a standard Foucault test apparatus. This paper presents graphical and numerical data that provide the necessary parameters for implementing the Ross null test for mirrors with focal ratios ranging from f/3.5 to f/10 and for conic deformations ranging from eccentricities of 0.70-1.50.

Byline: V. V. Makeev (1) Abstract: It is proved that each convex planar figure K a [].sup.2 contains a point O such that the perimeter of K computed with respect to the Minkowski distance function of the pair (K, O) is at most 9. If K is a triangle, this estimate is sharp. Bibliography: 7 titles. Author Affiliation: (1) St. Petersburg State University, St. Petersburg, Russia Article History: Registration Date: 05/10/2005 Received Date: 25/09/2003 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 262--266.

Byline: V. Ya. Lozynska (1) Abstract: It is established in the paper that the spaces of entire functions of exponential type generated by the operator of differentiation defined in the space of summable functions on the axis belong to the well-known Sebastian-e-Silva class of locally convex spaces. Some properties of the spaces relating to the duality and the open map theorem, as well as properties of convolution, are described. Author Affiliation: (1) Pidstrygach Institute of Applied Problems in Mechanics and Mathematics of the National Academy of Science of Ukraine, Lviv Article History: Registration Date: 20/10/2004

The unary predicates that can eliminate quantifiers are employed for the classification of the reducts of expansion (Q,

A large number of experiments and simulations were conducted to achieve the precise control of bending direction of the plate and to study the effect of the heating position and starting point on the bending direction.

Every tile-maker is a semi-tile maker by definition and all convex polyhedra that are tile-makers are determined. The convex polyhedra that could possibly be semi-tile makers are conjectured.

Two coffee cups, one convex and one concave were used to investigate a mathematical problem of properties of volumes of revolution. The result after calculations showed that volumes of both the cups were almost same.

The impact of the clubhead of a driver with a golf ball is modeled. The effect of the convex clubface of a driver on the flight of the golf ball is considered and the dependence of the optimum curvature of the clubface on the volume, mass, and impact speed of the clubhead is determined.

Abstract. We give a data structure that allows arbitrary insertions and deletions on a planar point set P and supports basic queries on the convex bull of P, such as […]

This paper studies the problem of [H.sub.2] norm checking for a MIMO system with parameter uncertainties. Under the assumptions that the coefficients of the numerator polynomial of the system's transfer function are multi-affine functions of the uncertain parameter that varies in a convex polytope, and that the coefficients of the denominator polynomial of the system's transfer function are affine functions of the uncertain parameter which varies in a convex polytope, a vertex checking result is obtained. Index Terms--Family of systems, [H.sub.2] norm, multi-affine, parameter uncertainties.

New constructions of convex directions for Hurwitz-stable polynomials are obtained. The technique is based on interpretations of the phase-derivative conditions in terms of the sensitivity of the root-locus associated with the even and odd parts of a polynomial. Index Terms--Convex direction, polynomials, robust control, stability.

In this paper, we present an extension to the uniform geometrical theory of diffraction (GTD) for reflection from smooth curved surfaces. This approach allows the source to be much closer to the reflecting surface than the conventional uniform GTD formulation and does not require a Hertzian dipole source. In essence, the field point is mirrored in the plane tangential to the specular (reflection) point; the incident field is then calculated at the mirror point and the uniform GTD reflection coefficients are used to mirror this field to the original field point. This formulation reduces exactly to the conventional uniform GTD if the incident field is ray optical. The application to a hybrid method of moments (MoM)/GTD code is outlined and results computed using this code are presented for a dipole radiating in the vicinity of a cylinder. Index Terms--Electromagnetic diffraction, geometrical theory of diffraction (GTD), method of moments, UTD.