The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has...The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.展开更多
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the...We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.展开更多
Trading rules performing well on a given data set seldom lead to promising out-of-sample results, a problem which is a consequence of the in-sample data snooping bias. Efforts to justify the selection of trading rules...Trading rules performing well on a given data set seldom lead to promising out-of-sample results, a problem which is a consequence of the in-sample data snooping bias. Efforts to justify the selection of trading rules by assessing the out-of-sample performance will not really remedy this predica- ment either, because they are prone to be trapped in what is known as the out-of-sample data-snooping bias. Our approach to curb the data-snooping bias consists of constructing a framework for trading rule selection using a-priori robustness strategies, where robustness is gauged on the basis of time- series bootstrap and multi-objective criteria. This approach focuses thus on building robustness into the process of trading rule selection at an early stage, rather than on an ex-post assessment of trading rule fitness. Intra-day FX market data constitute the empirical basis of the proposed investigations. Trading rules are selected from a wide universe created by evolutionary computation tools. The authors show evidence of the benefit of this approach in terms of indirect forecasting accuracy when investing in FX markets.展开更多
We obtain sufficient conditions for the existence of non-constant periodic solutions of the following planar system with four delays Our approach is based on the continuation theorem of the coincidence degree, and the...We obtain sufficient conditions for the existence of non-constant periodic solutions of the following planar system with four delays Our approach is based on the continuation theorem of the coincidence degree, and the a-priori estimate of periodic solutions.展开更多
文摘The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.
文摘We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.
文摘Trading rules performing well on a given data set seldom lead to promising out-of-sample results, a problem which is a consequence of the in-sample data snooping bias. Efforts to justify the selection of trading rules by assessing the out-of-sample performance will not really remedy this predica- ment either, because they are prone to be trapped in what is known as the out-of-sample data-snooping bias. Our approach to curb the data-snooping bias consists of constructing a framework for trading rule selection using a-priori robustness strategies, where robustness is gauged on the basis of time- series bootstrap and multi-objective criteria. This approach focuses thus on building robustness into the process of trading rule selection at an early stage, rather than on an ex-post assessment of trading rule fitness. Intra-day FX market data constitute the empirical basis of the proposed investigations. Trading rules are selected from a wide universe created by evolutionary computation tools. The authors show evidence of the benefit of this approach in terms of indirect forecasting accuracy when investing in FX markets.
文摘We obtain sufficient conditions for the existence of non-constant periodic solutions of the following planar system with four delays Our approach is based on the continuation theorem of the coincidence degree, and the a-priori estimate of periodic solutions.
