Contextualism on a pragmatic,not a skeptical,footing

Contextualism is supposed to explain why the following argument for skepticism seems plausible: (1) I don’t know that I am not a bodiless brain-in-a-vat (BIV); (2) If I know I have hands, then I know I am not a bodiless BIV; (3) Therefore, I do not know I have hands. Keith DeRose claims that (1) and (2) are “initially plausible.” I claim that (1) is initially plausible only because of an implicit argument that stands behind it; it is not intuitively plausible. The argument DeRose offers is based on the requirement of sensitivity, that is, on the idea that if you know something then you would not believe it if it were false. I criticize the sensitivity requirement thereby undercutting its support for (1) and the skeptical data that contextualism is meant to explain. While skepticism is not a plausible ground for contextualism, I argue that certain pragmatic considerations are. It’s plausible to think that to know something more evidence is required when more is at stake. The best way to handle skepticism is to criticize the arguments for it. We should not adopt contextualism as a means of accommodating skepticism even if there are other pragmatic reasons for being a contextualist about knowledge.     

Solution of the problems of a perforated disk,a conical bar,and a flat wedge of nonlinear viscoelastic material in pure shear,torsion, and bending,respectively

Exact solutions and approximations have been obtained for the problems of a disk with an opening twisted by opposite moments uniformly distributed over the inner and outer surfaces and of a conical bar twisted by a moment applied at the vertex of the cone. An approximate solution has been found for the problem of a flat wedge bent by pressure uniformly distributed along one of its sides. The disk is made of nonlinear viscoelastic material. In [1] it was proposed that problems for such a material be solved by the method of approximations. The rheological law of the nonlinear viscoelastic material of the cone and the wedge in Laplace—Carson transforms is the relation of the theory of small elastoplastic deformations with a power law of strain hardening.Institute of Electronic Engineering, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1076, November–December, 1971.     

[a,b]-factorization of a graph

Let a and b be integers such that 0 ? a ? b. Then a graph G is called an [a, b]-graph if a ? d_G(x) ? b for every x ? V(G), and an [a, b]-factor of a graph is defined to be its spanning subgraph F such that a ? d_F(x) ? b for every vertex x, where d_G(x) and d_F(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]-factors then we say that the graph is [2a, 2a]-factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)-factorable if and only if G is a [2am,2bm]-graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]-graph is [1,2]-factorable.     

Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design

A parting line for a polyhedron is a closed curve on its surface, which identifies the two halves of the polyhedron for which mold-boxes must be made. A parting line is undercut-free if the two halves that it generates do not contain facets that obstruct the de-molding of the polyhedron. Computing an undercut-free parting line that is as “flat” as possible is an important problem in mold design. In this paper, algorithms are presented to compute such a parting line for a convex polyhedron, based on different flatness criteria.     

Integration over a simplex,truncated cubes,and Eulerian numbers

Summary A method of integrating a function over a simplex is described in which (i) the simplex is first transformed into a right-angled isosceles simplex; (ii) this simplex is dissected into small cubes and truncated cubes; (iii) the integration over the truncated cubes is performed by the centroid method or by Stroud's method, and this requires the use of formulae for the moments of a truncated cube. These formulae are developed and are expressed in terms of Eulerian numbers. In the special case when the truncated cube is itself a right-angled isoceles simplex a new algorithm is given, depending on the discrete Fourier transform, for calculating the moments as polynomials inn wheren is the dimensionality.     

Analysis of a single-stage,single-product,stochastic, MRP-controlled assembly system

This paper models a single-stage, single-product, stochastic assembly system, operating according to an Materials Requirements Planning controlled (MRP) ordering philosophy. It deals explicitly with the underlying stochastic process that describes the end-product inventory position, enabling production lead times to be treated as independent and generally distributed random variables. The inventory position process is identified as a Markov renewal process, and this structure is exploited to determine system performance measures such as average inventory level, average backorder level, and the probability distribution of the end-product inventory position. An example, which demonstrates the type of analysis possible, focuses on quantifying the effect of kitting on the availability of end-products.     

A New Construction of Central Relative (p a , p a , p a , 1)-Difference Sets

Semiregular relative difference sets (RDS) in a finite group E which avoid a central subgroup C are equivalent to orthogonal cocycles. For example, every abelian semiregular RDS must arise from a symmetric orthogonal cocycle, and vice versa. Here, we introduce a new construction for central (p ^a , p ^a , p ^a , 1)-RDS which derives from a novel type of orthogonal cocycle, an LP cocycle, defined in terms of a linearised permutation (LP) polynomial and multiplication in a finite presemifield. The construction yields many new non-abelian (p ^a , p ^a , p ^a , 1)-RDS. We show that the subset of the LP cocycles defined by the identity LP polynomial and multiplication in a commutative semifield determines the known abelian (p ^a , p ^a , p ^a , 1)-RDS, and give a second new construction using presemifields.We use this cohomological approach to identify equivalence classes of central (p ^a , p ^a , p ^a , 1)-RDS with elementary abelian C and E/C. We show that for p = 2, a 3 and p = 3, a 2, every central (p ^a , p ^a , p ^a , 1)-RDS is equivalent to one arising from an LP cocycle, and list them all by equivalence class. For p = 2, a = 4, we list the 32 distinct equivalence classes which arise from field multiplication. We prove that, for any p, there are at least a equivalence classes of central (p ^a , p ^a , p ^a , 1)-RDS, of which one is abelian and a – 1 are non-abelian.     

Thermoelastic state of a medium,containing a thermally insulated ellipsoidal cavity,when subjected to a uniform heat flow

This article examines a problem of static thermoelasticity for an isotropic medium with an ellipsoidal cavity. The orientation of the cavity relative to the heat flow is assumed to be arbitrary. The solution of the problem is constructed in closed form and is expressed through incomplete elliptic integrals of the first and second kinds. In cases when the ellipsoid degenerates into a spheroid or sphere, the stress-strain state can be written in elementary functions of the ellipsoidal coordinate.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 46–50, 1988.     

Spanning cactus of a graph: Existence,extension, optimization,and approximation

We show that testing if an undirected graph contains a bridgeless spanning cactus is NP-hard. As a consequence, the minimum spanning cactus problem (MSCP) on an undirected graph with 0–1 edge weights is NP-hard. For any subgraph $S$ of $K_n$, we give polynomially testable necessary and sufficient conditions for $S$ to be extendable to a cactus in $K_n$ and the weighted version of this problem is shown to be NP-hard. A spanning tree is shown to be extendable to a cactus in $K_n$ if and only if it has at least one node of even degree. When $S$ is a spanning tree, we show that the weighted version can also be solved in polynomial time. Further, we give an $O\left(n^3\right)$ algorithm for computing a minimum cost spanning tree with at least one vertex of even degree on a graph on $n$ nodes. Finally, we show that for a complete graph with edge-costs satisfying the triangle inequality, the MSCP is equivalent to a general class of optimization problems that properly includes the traveling salesman problem and they all have the same approximation hardness.     

Subgroups,of Chevalley groups over a locally finite field,defined by a family of additive subgroups

It is proved that every elementary carpet of nonzero additive subgroups which is associated with a Chevalley group of a Lie rank exceeding one over a locally finite field coincides, up to conjugation by a diagonal element, with a carpetwhose additive subgroups are equal to some chosen subfield of the ground field. A similar result is obtained for a full matrix carpet (a full net).     

On (p a , p b , p a , p a-b )-Relative Difference Sets

This paper provides new exponent and rank conditions for the existence of abelian relative (p ^a,p ^b,p ^a,p ^a–b)-difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c–d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G Z₈ × Z₄ × Z₂ exists if and only if exp(G) 4 or G = Z₈ × (Z₂)³ with N Z₂ × Z₂.     

Nonlocal diffusion,a Mittag-Leffler function and a two-dimensional Volterra integral equation

In this paper we consider a particular class of two-dimensional singular Volterra integral equations. Firstly we show that these integral equations can indeed arise in practice by considering a diffusion problem with an output flux which is nonlocal in time; this problem is shown to admit an analytic solution in the form of an integral. More crucially, the problem can be re-characterized as an integral equation of this particular class. This example then provides motivation for a more general study: an analytic solution is obtained for the case when the kernel and the forcing function are both unity. This analytic solution, in the form of a series solution, is a variant of the Mittag-Leffler function. As a consequence it is an entire function. A Gronwall lemma is obtained. This then permits a general existence and uniqueness theorem to be proved.     

Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator

The discontinuous dynamics of a non-linear, friction-induced, periodically forced oscillator is studied. The analytical conditions for motion switchability at the velocity boundary in such a nonlinear oscillator are developed to understand the motion switching mechanism. Using such analytical conditions of motion switching, numerical predictions of the switching scenarios varying with excitation frequency and amplitude are carried out, and the parameter maps for specific periodic motions are presented. Chaotic and periodic motions are illustrated through phase planes and switching sections for a better understanding of motion mechanism of the nonlinear friction oscillator. The periodic motions with switching in such a nonlinear, frictional oscillator cannot be obtained from the traditional analysis (e.g., perturbation and harmonic balance method).     

Maximization,under equality constraints,of a functional of a probability distribution

Let $\text{F}$ be a family of probability distributions. Let O, C₁…C_n be real functions on $\text{F}$. Let z₁…z_n be real numbers. Then we consider the problem of maximization of the object function O(F)(F?$\text{F}$) under the equality constraints C₁(F)=z₁(i=1,…,n) . The theory is developed in order to solve problems of the following kind: Find the maximal variance of a stop-loss reinsured risk under partial information on the risk such as its range and two first moments.     

Distance-regular graphs and (s,c, a,k)-graphs

A diameter-bound theorem for a class of distance-regular graphs which includes all those with even girth is presented. A new class of graphs, called (s, c, a, k)-graphs, is introduced, which are conjectured to contain enough of the local structure of finite distance-regular graphs for them all to be finite. It is proved that they are finite and a bound on the diameter is given in the case a ≤ c.     

Permutation Groups, a Related Algebra and a Conjecture of Cameron

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special cases, including those of the form H Wr S and H Wr A, and show that in the oligormorphic case, the algebras corresponding to these special groups are polynomial algebras. In the H Wr A case, the algebra is related to the shuffle algebra of free Lie algebra theory.     

The Rotation of a Gravitating Sphere in a Monatomic Gas,I

The flow resulting from the steady rotation of a gravitating sphere in a monatomic gas is studied in two special cases. If the rotation is slow, then the motion consists of a swirling flow whose streamlines are concentric circles around the rotation axis, and a slower meridional flow whose structure depends on the strength of the gravitational field. This meridional flow is investigated in detail for small and large field strength. In the latter case, the scale height is small compared to the sphere radius, and most of the fluid is in a thin recirculating layer on the surface. However, the mathematics imposes a severe restriction on the rotation speed if the field is large, which leads to a more general investigation of the flow for very large field strength, i.e. for a thin “atmosphere”. Compressibility effects can be quite sizeable in this final solution. Though a thin recirculating surface layer still exists in only slightly modified form, the fluid outside this layer is much less tenuous than for the case when the rotation is slow. The flow in the region outside the boundary layer involves solution of two quasilinear elliptic equations.     

Split skew products,a related functional equation,and specification

We prove that a skew product of a measure-preserving transformation with an ergodic automorphism of a compact abelian group is always isomorphic to their direct product via an isomorphism that merely translates the group fibers. This requires solving a functional equation. A weak version of Bowen’s specification property is essential to our construction of a solution.