A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
We study properties of the fourth rank elasticity tensor C within linear elasticity theory. First C is irreducibly decomposed under the linear group into a Cauchy piece S (with 15 independent components) and a non-Cauchy piece A (with 6 independent c
omponents). Subsequently, we turn to the physically relevant orthogonal group, thereby using the metric. We find the finer decomposition of S into pieces with 9+5+1 and of A into those with 5+1 independent components. Some reducible decompositions, discussed earlier by numerous authors, are shown to be inconsistent. --- Several physical consequences are discussed. The Cauchy relations are shown to correspond to A=0. Longitudinal and transverse sound waves are basically related by S and A, respectively.
Dynamic programming languages, such as PHP, JavaScript, and Python, provide built-in data structures including associative arrays and objects with similar semantics-object properties can be created at run-time and accessed via arbitrary expressions.
While a high level of security and safety of applications written in these languages can be of a particular importance (consider a web application storing sensitive data and providing its functionality worldwide), dynamic data structures pose significant challenges for data-flow analysis making traditional static verification methods both unsound and imprecise. In this paper, we propose a sound and precise approach for value and points-to analysis of programs with associative arrays-like data structures, upon which data-flow analyses can be built. We implemented our approach in a web-application domain-in an analyzer of PHP code.
We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic
term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.
We derive a noncovariant but simple representation for the self-energy of a conformally transformed graviton field on the cosmological patch of de Sitter. Our representation involves four structure functions, as opposed to the two that would be neces
sary for a manifestly de Sitter invariant representation. We work out what the four structure functions are for the one loop correction due to a massless, minimally coupled scalar. And we employ the result to work out what happens to dynamical gravitons.
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of asymptotic no
rmality, Berry-Esseen bound, Edgeworth asymptotic expansions under weakened conditions and Cramer type large deviation results are derived.
We explore the cosmological consequences of some possible big bang produced by a black-hole with mass $M$ in an 5D extended SdS. Under these particular circumstances, the effective 4D metric obtained by the use of a constant foliation on the extra co
ordinate is comported as a false white-hole (FWH), which evaporates for all unstable modes that have wavelengths bigger than the size of the FWH. Outside the white hole the repulsive gravitational field can be considered as weak, so that the dynamics for fluctuations of the inflaton field and the scalar perturbations of the metric can be linearized.
A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Two ways to eliminate the using of such names in certain cases are indicated in
the paper. The first one is intended for the case of topological spaces with selected indexed denumerable bases. Suppose a partial function is given from one such space into another one whose selected base has a recursively enumerable index set, and suppose that the intersection of base open sets in the first space is computable in the sense of Weihrauch-Grubba. Then the ordinary TTE computability of the function is characterized by the existence of an appropriate recursively enumerable relation between indices of base sets containing the argument value and indices of base sets containing the corresponding function value.This result can be regarded as an improvement of a result of Korovina and Kudinov. The second way is applicable to metric spaces with selected indexed denumerable dense subsets. If a partial function is given from one such space into another one, then, under a semi-computability assumption concerning these spaces, the ordinary TTE computability of the function is characterized by the existence of an appropriate recursively enumerable set of quadruples. Any of them consists of an index of element from the selected dense subset in the first space, a natural number encoding a rational bound for the distance between this element and the argument value, an index of element from the selected dense subset in the second space and a natural number encoding a rational bound for the distance between this element and the function value. One of the examples in the paper indicates that the computability of real functions can be characterized in a simple way by using the first way of elimination of the infinitistic names.
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the component
theories. As such, they extend the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several contexts; in particular, in the semantics of programming languages, the monad transformer for global state is given by a tensor. We present two main results: we show that the tensor of two monads need not in general exist by presenting two counterexamples, one of them involving finite powerset (i.e. the theory of join semilattices); this solves a somewhat long-standing open problem, and contrasts with recent results that had ruled out previously expected counterexamples. On the other hand, we show that tensors with bounded powerset monads do exist from countable powerset upwards.
Cross-training workers is one of the most efficient ways to achieve flexibility in manufacturing and service systems to increase responsiveness to demand variability. However, it is generally the case that cross-trained employees are not as productiv
e as employees who are originally trained on a specific task. Also, the productivity of the cross-trained workers depend on when they are cross-trained. In this work, we consider a two-stage model to analyze the affect of variations in productivity levels of workers on cross-training policies. Our results indicate that the most important factor determining the problem structure is the consistency in productivity levels of workers trained at different times. As long as cross-training can be done in a consistent manner, the productivity differences between cross-trained workers and workers originally trained on the task plays a minor role. We also analyze the effect of the variabilities in demand and producivity levels. We show that if the productivity levels of workers trained at different times are consistent, the decision maker is inclined to defer the cross-training decisions as the variability of demand or productivity levels increases. However, when the productivities of workers trained at different times differ, the decision maker may prefer to invest more in cross-training earlier as variability increases.
