scholarly journals THE RAMIFIED ANALYTICAL HIERARCHY USING EXTENDED LOGICS

2018 ◽  
Vol 24 (3) ◽  
pp. 306-318
Author(s):  
PHILIP D. WELCH
Keyword(s):  
Minimal Model ◽  
Wide Spectrum ◽  
Second Order ◽  
Similar Investigation ◽  
Constructible Sets ◽  
The Given

AbstractThe use of Extended Logics to replace ordinary second order definability in Kleene’s Ramified Analytical Hierarchy is investigated. This mirrors a similar investigation of Kennedy, Magidor and Väänänen [11] where Gödel’s universe L of constructible sets is subjected to similar variance. Enhancing second order definability allows models to be defined which may or may not coincide with the original Kleene hierarchy in domain. Extending the logic with game quantifiers, and assuming strong axioms of infinity, we obtain minimal correct models of analysis. A wide spectrum of models can be so generated from abstract definability notions: one may take an abstract Spector Class and extract an extended logic for it. The resultant structure is then a minimal model of the given kind of definability.

The features of transnational corporations’ advertisement in social networks

2019 ◽  
pp. 89-92
Author(s):  
Daniella Mushka ◽  
Yeva Erfan
Keyword(s):  
Social Networks ◽  
Social Media ◽  
Wide Spectrum ◽  
Subsequent Development ◽  
Transnational Corporations ◽  
Target Audience ◽  
Social Media Marketing ◽  
Scientific Article ◽  
The Social ◽  
The Given

This scientific article considers all aspects, modern importance and growing role of the social media marketing and advertisement in the general spectrum of marketing activity for developed and developing brands. Investigational actuality and basic directions of application of all spectrum of instruments of social networks for the sake of advancement of product and the processes of forming perception of trade mark and forming the image of brand are analyzed by the authors of the article. The given scientific article highlights the most popular trends and patterns of goods and trademarks’ promotion in the world in the context of updating the concept of advertising on social networks. The bigger and more engaged your target audience is on social media networks (Instagram, Facebook, Twitter, YouTube etc), the easier it will be for you to achieve every other marketing or business goal. The importance of social media marketing’s assistance in attracting new potential clients and customers to the company is also considered in the given article. Besides that, the authors of the article list and analyse wide spectrum of basic trends considering promotion and advertising in 2019 among the well-known brands. In addition to this all, the list of the most successful publicity advertisement campaigns of this year and brands which were promoted with their assistance are listed and analysed. In the context of the study, it shows up that advertising campaigns play a significant role not only in reaching sales but also in generating overall customer loyalty to the brand. This makes it possible to argue that the most reputable brands should have an important social goal that will be positively accepted by society and target audience in addition to the high quality and usability of the products or services. Social networking is the easiest way to see the social response to your promotion and lead to an instant purchase. Therefore, relying on the experience of the already well-known multinational and transnational corporations, social media marketing should take a significant share of the overall promotion of the company. The connection between the brand and potential customer should be built on the emotions that accompany consumers when viewing ads and using products. This scientific article eventually declares conclusions and prognoses in relation to subsequent development of these instruments and platforms for advancement and branding of small and large enterprises in future. It states that emotional connection between person and brand is much more effective for the company than an expensive ad.

SURFACE-COVERED 1×3 GRATING WITH DIELECTRIC-METAL SLABS UNDER SECOND BRAGG INCIDENCE

2020 ◽  
Vol 27 (09) ◽  
pp. 1950201
Author(s):  
CHEN FU ◽  
BO WANG ◽  
WENHUA ZHU ◽  
KUNHUA WEN ◽  
ZIMING MENG ◽  
...  
Keyword(s):  
Incident Light ◽  
Polarized Light ◽  
Transverse Magnetic ◽  
Second Order ◽  
Bragg Angle ◽  
Efficiency Ratio ◽  
First Order ◽  
Rigorous Coupled Wave Analysis ◽  
Rigorous Coupled Wave ◽  
The Given

This paper designed a novel three-port reflective surface-covered grating with a connecting layer. The grating can be used as a splitter, and the polarized light can be divided into zero order, first order and second order. Through rigorous coupled-wave analysis, the efficiency of the three orders of diffraction light is close to 33% under the condition that the incident light at 1550 nm is incident at the second Bragg angle and the given duty cycle is 0.5. The efficiency and bandwidth of the surface-covered grating are improved compared with that of the surface-relief grating reported in the past. Especially for transverse magnetic polarized light, the beam splitting effect is more uniform, the efficiency ratio of the zeroth order to first order can reach 1.01, and the efficiency ratio of the first order to second order can reach 1.

scholarly journals Sampled-Data-Based Adaptive Group Synchronization of Second-Order Nonlinear Complex Dynamical Networks with Time-Varying Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Bo Liu ◽  
Jiahui Bai ◽  
Yue Zhao ◽  
Chao Liu ◽  
Xuemin Yan ◽  
...  
Keyword(s):  
Adaptive Strategy ◽  
Second Order ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Sampled Data ◽  
Dynamical Networks ◽  
Coupling Strengths ◽  
Simulation Results ◽  
Group Synchronization ◽  
The Given

This paper studies the adaptive group synchronization of second-order nonlinear complex dynamical networks with sampled-data and time-varying delays by designing a new adaptive strategy to feedback gains and coupling strengths. According to Lyapunov stability properties, it is shown that the agents of subgroups can converge the given synchronous states, respectively, under some conditions on the sampled period. Moreover, some simulation results are given.

Uniformly almost periodic solutions of non-linear differential equations of the second order I. General exposition

1955 ◽  
Vol 51 (4) ◽  
pp. 604-613
Author(s):  
Chike Obi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential ◽  
The Given ◽  
Analytical Expressions

1·1. A general problem in the theory of non-linear differential equations of the second order is: Given a non-linear differential equation of the second order uniformly almost periodic (u.a.p.) in the independent variable and with certain disposable constants (parameters), to find: (i) the non-trivial relations between these parameters such that the given differential equation has a non-periodic u.a.p. solution; (ii) the number of periodic and non-periodic u.a.p. solutions which correspond to each such relation; and (iii) explicit analytical expressions for the u.a.p. solutions when they exist.

scholarly journals Logics with Multiteam Semantics

2022 ◽  
Vol 23 (2) ◽  
pp. 1-30
Author(s):  
Erich Grädel ◽  
Richard Wilke
Keyword(s):  
Wide Spectrum ◽  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Specific Class ◽  
Mathematical Basis ◽  
Logical Operators ◽  
Team Semantics ◽  
Independence Properties ◽  
Second Order Logic

Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters, but being based on sets, it does not take into account multiple occurrences of data values. It is therefore insufficient in scenarios where such multiplicities matter, in particular for reasoning about probabilities and statistical independencies. Therefore, an extension from teams to multiteams (i.e. multisets of assignments) has been proposed by several authors. In this paper we aim at a systematic development of logics of dependence and independence based on multiteam semantics. We study atomic dependency properties of finite multiteams and discuss the appropriate meaning of logical operators to extend the atomic dependencies to full-fledged logics for reasoning about dependence properties in a multiteam setting. We explore properties and expressive power of a wide spectrum of different multiteam logics and compare them to second-order logic and to logics with team semantics. In many cases the results resemble what is known in team semantics, but there are also interesting differences. While in team semantics, the combination of inclusion and exclusion dependencies leads to a logic with the full power of both independence logic and existential second-order logic, independence properties of multiteams are not definable by any combination of properties that are downwards closed or union closed and thus are strictly more powerful than inclusion-exclusion logic. We also study the relationship of logics with multiteam semantics with existential second-order logic for a specific class of metafinite structures. It turns out that inclusion-exclusion logic can be characterised in a precise sense by the Presburger fragment of this logic, but for capturing independence, we need to go beyond it and add some form of multiplication. Finally, we also consider multiteams with weights in the reals and study the expressive power of formulae by means of topological properties.

scholarly journals Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Root Functions ◽  
Riesz Property ◽  
System Of Root Functions ◽  
The Given ◽  
Riesz Inequality

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

scholarly journals Action Function Formulation for Conservative Systems with Second-Order Lagrangian

2018 ◽  
Vol 10 (4) ◽  
pp. 50
Author(s):  
Ola Jarabah
Keyword(s):  
Lagrange Equation ◽  
Equations Of Motion ◽  
Second Order ◽  
Action Function ◽  
Time Integral ◽  
Function Formulation ◽  
Conservative Systems ◽  
The Given

The Euler Lagrange equation is studied to obtain the equations of motion for conservative systems with second order Lagrangian. The solutions of these equations are substituted in the given Lagrangian. The action function is then derived by calculating the time integral of the Lagrangian. To explain the application of our formalism two examples are discussed.

Synthesis and Optimization of Transient Performances for Underdamped Second-Order Linear System Based on the Switching Control Strategy

2012 ◽  
Author(s):  
Qingyu Su ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Optimization Problems ◽  
Switching Control ◽  
Second Order ◽  
Order Linear ◽  
Output Response ◽  
Special Cases ◽  
Switching Control Strategy ◽  
The Given

In this paper, the synthesis and optimization problems of the transient performances, such as overshoot and setting time, of the output response with respect to a step signal for an under-damped second-order linear system are studied. The traditional control strategy and the switching control strategy are used, respectively. Our control objective is twofold: Objective 1 is to ensure that the overshoot of the system output does not violate the given safety bound and objective 2 is to ensure that the settling time is smaller than the given allowable time. The obtained results indicate that the switching control strategy has main two evident advantages: firstly, the switching proportional controllers can take advantages of both the quick response and the small overshoot of the output response. Secondly, the switching controller is always available, while the single proportional controller is available in some special cases. Finally, an example of servomotor is given to demonstrate the effectiveness of the proposed method.

scholarly journals RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES

2014 ◽  
Vol 79 (3) ◽  
pp. 712-732 ◽  
Author(s):  
SATO KENTARO
Keyword(s):  
Number Theory ◽  
Set Theory ◽  
Higher Order ◽  
Second Order ◽  
Order Number ◽  
Recursion Scheme ◽  
Transfinite Recursion ◽  
The Given ◽  
The Universe ◽  
Order Set

AbstractThis article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

scholarly journals INVESTIGATION OF SOME CLASSES OF SECOND ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH A POWERLOGARITHMIC SINGULARITY IN THE KERNEL

2020 ◽  
pp. 40-54
Author(s):  
Sarvar K. ZARIFZODA ◽  
◽  
Raim N. ODINAEV ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Differential Operators ◽  
Logarithmic Singularity ◽  
Second Order ◽  
Fredholm Type ◽  
Power Singularity ◽  
Characteristic Equations ◽  
Integro Differential Equation ◽  
The Given

For a class of second-order partial integro-differential equations with a power singularity and logarithmic singularity in the kernel, integral representations of the solution manifold in terms of arbitrary constants are obtained in the class of functions vanishing with a certain asymptotic behavior. Although the kernel of the given equation is not a Fredholm type kernel, the solution of the studied equation in a class of vanishing functions is found in an explicit form. We represent a second-order integro-differential equation as a product of two first-order integro-differential operators. For these one-dimensional integro-differential operators, in the cases when the roots of the corresponding characteristic equations are real and different, real and equal and complex and conjugate, the inverse operators are found. It is found that the presence of power singularity and logarithmic singularity in the kernel affects the number of arbitrary constants in the general solution. This number, depending on the roots of the corresponding characteristic equations, can reach nine. Also, the cases when the given integro-differential equation has a unique solution are found. The correctness of the obtained results with the help of the detailed solutions of concrete examples are shown. The method of solving the given problem can be used for solving model and nonmodel integro-differential equations with a higher order power singularity and logarithmic singularity in the kernel.

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