Arithmetic Examples Research Articles

Reliability analysis under constant-stress partially accelerated life tests using hybrid censored data from Weibull distribution

This article discusses the estimation of Weibull distribution parameters based on hybrid censored data under constant-stress partially accelerated test model. Two estimation methods; maximum likelihood (ML) and percentile bootstrap (PB) are used to make statistical inference on the Weibull distribution parameters and the acceleration factor. The mean square errors of the estimators are calculated to evaluate their performances through a Monte Carlo simulation study. Moreover, the confidence intervals lengths (CILs) and their associated coverage probabilities (CPs) are obtained. Finally, to demonstrate the proposed methodology, an arithmetic example is given.

Vertical vibration of an elastic pile embedded in poroelastic soil

We present an analytical study on the vertical vibration of an elastic pile embedded in poroelastic soil. The poroelastic soil is divided into a homogeneous half-space underlying the pile base and a series of infinitesimally thin independent layers along its shaft. The dynamic interaction problem is solved by extending a method originally proposed for an embedded rigid foundation. The validity of the derived solution is verified via comparison with existing solutions. Arithmetical examples are used to demonstrate the sensitivity of the vertical pile impedance to the relative rigidity of the two soil parts.

Arithmetic, Mathematical Intuition, and Evidence

This paper provides examples in arithmetic of the account of rational intuition and evidence developed in my book After Gödel: Platonism and Rationalism in Mathematics and Logic (Oxford: Oxford University Press, 2011). The paper supplements the book but can be read independently of it. It starts with some simple examples of problem-solving in arithmetic practice and proceeds to general phenomenological conditions that make such problem-solving possible. In proceeding from elementary ‘authentic’ parts of arithmetic to axiomatic formal arithmetic, the paper exhibits some elements of the genetic analysis of arithmetic knowledge that is called for in Husserl’s philosophy. This issues in an elaboration on a number of Gödel’s remarks about the meaning of his incompleteness theorems for the notion of evidence in mathematics.

Derivation of the radial gradient of the gravity based on non-full tensor satellite gravity gradients

The formula for computing the radial gradient of the gravity is derived from the gravity gradients. Since GOCE satellite attitude has such property that one axis in the gradiometer almost has the same direction as the radial one of the earth, the formula can be used to compute the radial derivative of second order of the disturbing potential. This means that the boundary value problem (BVP) with the radial gradient of the gravity can be established on the satellite orbit. Hence, the recovery of the gravity field from GOCE data can be realized by solving the BVP. In order to examine the accuracy of the BVP, an arithmetic example is given, the computational results of which illustrate that the efficient degrees/orders of the gravity field model recovered by the BVP can satisfy the requirements of the satellite gravity gradients. In addition, a gravity field model is solved out from the BVP by using actual GOCE data.

Questions on the geometry of finite coherence

In this article, we indicate that in any two-period model of financial markets with a finite state space, we may define a variety of coherent risk measures on the payoff space of the market. These risk measures depend on the Equivalent or on the Generalized Equivalent Martingale Measures of the market. We also present some examples which illustrate the multiplicity of the coherent risk measures, which depends on the extreme points of the set of the Generalized Martingale Measures of a market, if this market is arbitrage free. We actually present in a systematic way the previous connection jointly with the examples, while the origins of these ideas come from the work of Artzner et al. (1999). We also present an aspect of this connection related to the finite -dimensional Expected Shortfall, relying on the dual representation of it and we provide arithmetic examples, too.

Research on UCAV Efficiency Evaluation Method

UCAV will play a more and more important role in future fight. UCAV efficiency evaluation method is still in the developing stage. UCAV fight elements are analyzed that include reconnaissance elements and attacking to ground elements. Basing on analysis of UCAV reconnaissance efficiency and attacking ground efficiency, UCAV reconnaissance efficiency model and attacking ground efficiency model are constructed. The feasibility and validity of model is validated by arithmetic example.

The integral formulas of the associated Legendre functions

A new kind of integral formulas for $${\bar{P}_{n,m} (x)}$$ is derived from the addition theorem about the Legendre Functions when n − m is an even number. Based on the newly introduced integral formulas, the fully normalized associated Legendre functions can be directly computed without using any recursion methods that currently are often used in the computations. In addition, some arithmetic examples are computed with the increasing degree recursion and the integral methods introduced in the paper respectively, in order to compare the precisions and run-times of these two methods in computing the fully normalized associated Legendre functions. The results indicate that the precisions of the integral methods are almost consistent for variant x in computing $${\bar{P}_{n,m} (x)}$$ , i.e., the precisions are independent of the choice of x on the interval [0,1]. In contrast, the precisions of the increasing degree recursion change with different values on the interval [0,1], particularly, when x tends to 1, the errors of computing $${\bar{P}_{n,m} (x)}$$ by the increasing degree recursion become unacceptable when the degree becomes larger and larger. On the other hand, the integral methods cost more run-time than the increasing degree recursion. Hence, it is suggested that combinations of the integral method and the increasing degree recursion can be adopted, that is, the integral methods can be used as a replacement for the recursive initials when the recursion method become divergent.

A Simulated Study of the Influence of Wind Projecting Angle on Energy Consumption of Residential Building Clusters

In the study of cluster thermal environment, the projecting angle of wind against buildings exercises vital influence on the environment. This thesis, taking Xi’an region as a representative city, conducts a study of how different wind projecting angles influence the thermal environment by means of the simulator program of energy consumption. By sequentially alternating the included angle between the orientation of building cluster and wind direction, it sets up different arithmetic example models which can meet the requirements of various seasons. It also quantitatively expounds the impact of wind projecting angle on energy consumption of buildings with the annual minimal energy consumption of buildings as its basis. The research has worked out the following recommended plans about the orientation of cluster distribution in Xi’an region. The building is at its lowest level of energy consumption when its wind projecting angle is 30 degrees. Its energy consumption is relatively stable when its wind projecting angle is 45 degrees or when it rotates anti-clockwise within 15 degrees.

Three Views of Theoretical Knowledge

Of the three views of theoretical knowledge which form the focus of this article, the first has its source in the work of Russell, the second in Ramsey, and the third in Carnap. Although very different, all three views subscribe to a principle I formulate as ‘the structuralist thesis’; they are also naturally expressed using the concept of a Ramsey sentence. I distinguish the framework of assumptions which give rise to the structuralist thesis from an unproblematic emphasis on the importance of ‘structural’ differences for the analysis and interpretation of theories belonging to the exact sciences, and I review a number of logical properties of Ramsey sentences using very simple arithmetical theories and their models. I then develop a reconstruction of the views of Russell, Ramsey, and Carnap that clarifies the interrelationships among them by appealing to aspects of the arithmetical examples that inform my discussion of Ramsey sentences. I conclude with an account of the philosophical basis of the structuralist thesis and the fundamental difficulty to which it leads. 1 Introduction2 Ramsey Sentences and Craig Transcriptions3 Ramsey Sentences and the Applications of a Theory4 Extensions and Expansions of Models and Russell’s Structuralism5 Ramsey on Theories6 Carnap’s Synthesis7 The Structuralist Thesis

COMPUTABLE STRUCTURES OF RANK $\omega_{1}^{{\rm CK}}$

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks.

The gravitational gradient tensor’s invariants and the related boundary conditions

Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O(J22· T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10−7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10−8 and the order can reach up to 280.

A practical geometrical comparison between free-repelled hydraulic jumps within inclined channels

In this experimental study a practical geometrical comparison between inclined (angle φ) free and repelled hydraulic jumps (the latter in non prismatic but abruptly expanding channels) is presented, analysed and discussed. For repelled hydraulic jumps a considerable parameter is the expansion ratio r (=channels’ width ratio), which here is changing from r =0.5 to r =0.7. The comparison is made with the free jump (in prismatic channel, r =1), in the same ranges of angles φ (0° ⩽ φ ⩽8°) and Froude numbers (2⩽Fr 1⩽8). A practical arithmetic example is presented to show the behavioral change of conjugate depths, lengths L and depths at 0.5L, in order to receive a comparison among all pertinent geometrical quantities. The present results may be useful for the hydraulic engineering when designing open channels.

A model for calculating the temperature of aluminium particles ejected from overhead low-voltage lines owing to a short-circuit

Wildfires, which are uncontrolled fires spreading readily over vast areas, are usually the result of human negligence, arson or lightning. There are cases of fires close to electrical distribution lines for which the network has been blamed. In the present paper, the risk of a wildfire breaking out owing to the temperature of molten metal particles that are possibly created on bare conductors of low-voltage networks in short-circuit faults (unless they are interrupted by the protection systems) is examined. Thus, a mathematical model is proposed for the estimated temperature rise of those molten metal particles ejected from bare conductors of low-voltage overhead lines. Moreover, this model can be applied to medium- or high-voltage networks. The model takes into account the weather conditions and particles’ height above the ground. Further, an arithmetic example for an incandescent particle ejected from aluminium conductors of a low-voltage network is given. According to this example, there is no risk of dead leaves or wood catching fire owing to this particle.

Variational solution about over-determined geodetic boundary value problem and its related theories

Abstract A new solving method is studied by minimizing the quadratic functional in the paper. At first, the so-called calculus solution of over-detemined gedetic boundary value problem is introduced with help of variation principle, and various theoretical properties of it are discussed. Then the general way to compute it is given, and particularly, we can obtain its analytical expression under the case that boundary are all spheres. At last, an arithmetic example is constituted with EGM96 gravity model and computive result illustrates that the method can

Shared Waters—shared Responsibility. Application of the Principles of Fairness for Burden Sharing in the Mediterranean

The paper addresses the issue of burden sharing within the context of the Barcelona Convention for the protection of the Mediterranean. The initial premise is that the perceived fairness of burden sharing rules is an important factor in the success of multilateral environmental agreements. We review briefly the basic ideas behind the fairness and equity debate in global environmental affairs before we apply a number of widely accepted equity rules in the case of Mediterranean marine protection. We derive arithmetic examples to illustrate the application of the rules and compare them in terms of their political attractiveness, cost-effectiveness and practical feasibility. It is shown that the simple rule of egalitarian justice scores high on all aspects.

Connection Management Based on Gnutella Network

Gnutella is a fully decentralized and unstructured peer-to-peer network. It uses the message broadcasting mechanism of flooding. However, while bringing Gnutella network the characters of high degree of robustness and dynamic, this broadcasting mechanism makes the network give redundant messages that increase exponentially. On basis of resolving Gnutella network message broadcasting mechanism, the paper points out the necessity and feasibility of Gnutella network losing contact, and then bring forward the means which can compartmentalize Gnutella network message's PRI according to the transmitting bandwidth, the time, and the resources which are consumed by servents dealing with all kinds of messages. F-Measure is introduced to connection management, which is usually used to evaluate the performance of searching engine. The paper provides a discarding connection management algorithm, which discards the redundant connection by computation and ensures the maximal attainability of message simultaneously. Finally, the arithmetic example and discussion are given.

Do Fundamentals Explain the Behaviour of the Swedish Real Effective Exchange Rate?

AbstractThis study examines the long‐run relationship between the real effective exchange rate and its fundamental determinants, and derives a real effective equilibrium exchange rate for the Swedish krona. Our results indicate that the krona was severely overvalued in late 1992, when the fixed exchange rate regime was abandoned. By the end of 2000 the krona was undervalued by approximately 5 percent, given the prevailing economic conditions. Arithmetic examples of suitable SEK/EUR conversion rates are calculated under various assumptions to provide a guideline if Sweden were to adopt the euro in the future.

A Functional Algebraic Model Equivalent to Kleene's Slash Realizability

In one of his papers, Dragalin proposed a very general approach to the construction of models for nonstandard logics of uniform-algebra type and, in particular, for intuitionistic logic (see [1]). The presentation (clear enough, but without the obvious details) is accompanied by a number of arithmetical examples (see also [1]). In the last of these examples, Kleene’s slash realizability is considered (see [2, column C]), and the author gives a “ . . . model corresponding to Kleene’s slash realizability . . . ” [1, p. 194]. However, the connection between this model and Kleene’s slash realizability is as follows: “ . . . ‖φ‖ = T ⇔ ((|φ)∧HA φ)”; (see also [1, p. 195]; cf. [3]). Of course, by means of the above-mentioned model (which corresponds exactly to the formula realizability from [3]) one can prove the properties of disjunctiveness and existentiality for arithmetic (this is just the result the author seeks to obtain, using a suitable uniform algebra). However, Kleene’s slash realizability does not coincide with deducibility in the intuitionistic HA arithmetic. As mentioned above, the paper [1] contains a number of examples of functional pseudoboolean algebras corresponding to various HA models (including, in particular, realizability models). Exact formulation of functional pseudoboolean algebra is given in [1], and here we shall only briefly mention facts needed in what follows. If F is the set of forms of a functional pseudoboolean algebra, then for any f and g from F (where f and g are forms of the same arity), there exist the forms f ∧ g , f ∨ g , f ⊃ g in F of equal arity. After that, a functional algebraic model for logic-mathematical language is defined, and for a given functional algebraic model, we define the value of any formula of our language in it. The main distinction from usual algebraic models is in the fact that the value ‖φ‖ of the formula φ is a certain form fφ from a functional pseudoboolean algebra. Now we can fix the language of arithmetic, the object area, and the function Ĉnst . After that, each model is defined by specifying the following set: B (a pseudoboolean algebra), F , and Pr-valuation of predicates. Let a given functional pseudoboolean algebra be a model for Kleene’s slash realizability, i.e., suppose formulas of the language can be mapped to the set of forms so that any formula φ is |realizable if and only if fφ ∈ 1 (the unit of algebra B). Consider two distinct statements, φ and ψ , undecidable in HA, i.e., HA φ, HA ψ, HA ¬φ, HA ¬ψ. Since φ and ψ cannot be deduced in HA, the formulas ¬φ and ¬ψ are nondeducible |-realizable formulas of the language of arithmetic. If the forms corresponding to them in the functional algebraic model are F¬φ and F¬ψ , respectively, then these forms belong to algebra’s 1 , and then the form F¬φ ∨F¬ψ = F¬φ∨¬ψ (which corresponds in the functional algebraic model to the formula ¬φ∨¬ψ , see [1, p. 187]), also belongs to our algebra’s unit, and hence, the formula ¬φ∨¬ψ is |realizable. But this implies that HA φ or HA ψ , which is impossible by the choice of φ and ψ . Thus, we have proved the following theorem:

Curves of Genus 2 with (N, N) Decomposable Jacobians

Let C be a curve of genus 2 and ψ1: C −→E1 a map of degree n, from C to an elliptic curveE1 , both curves defined over C. This map induces a degree n map φ1:P1 −→P1 which we call a Frey–Kani covering. We determine all possible ramifications for φ1. If ψ1:C −→E1 is maximal then there exists a maximal map ψ2: C −→E2 , of degree n, to some elliptic curveE2 such that there is an isogeny of degree n2from the JacobianJC to E1×E2. We say thatJC is (n, n)-decomposable. If the degree n is odd the pair (ψ2, E2) is canonically determined. For n= 3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable.

Tozer on machinery

This paper examines John Edward Tozer's mathematical treatment of the classical approach to the machinery problem and his discussion of some arithmetical examples that had been presented by Barton, Sismondi, McCulloch and Ricardo. It is shown that Tozer (1) made a genuine contribution to the contemporary debates on the machinery issue, (2) anticipated modern formulations of the problem of the choice of technique, and (3) revealed a puzzling inconsistency in Ricardo's argument in the famous chapter ‘On Machinery’.