Plasmonic sensor with self-reference capability based on functional layer film composed of Au/Si gratings

We propose a simple one-dimensional grating coupling system that can excite multiple surface plasmon resonances for refractive index(RI)sensing with self-reference characteristics in the near-infrared band.Using theoretical analysis and the finite-difference time-domain method,the plasmonic mechanism of the structure is discussed in detail.The results show that the excited resonances are independent of each other and have different fields of action.The mode involving extensive interaction with the analyte environment achieves a high sensitivity of 1236 nm/RIU,and the figure of merit(FOM)can reach 145 RIU-1.Importantly,the mode that is insensitive to the analyte environment exhibits good self-reference characteristics.Moreover,we discuss the case of exchanging the substrate material with the analyte environment.Promising simulation results show that this RI sensor can be widely deployed in unstable and complicated environments.

An experimental study on the self-reference effect

Self-reference at encoding increases the probability of recollective experience in recognition memory. Self-reference effect (SRE) in memory is observed when the degree of self-refer- ence of to-be-remembered materials is varied. Usually items encoded in terms of self-reference are associated with significantly higher recall performance relative to items encoded in other ways, including semantic encoding. In our three experiments, four orientating tasks formed four levels in a between-subjects design. The conditions were rating personality traits with reference to self, mother, Lu Xun (a famous Chinese writer) or rating the traits on a negative-positive dimension. In a recognition test, subjects first identified old items and then indicated which of these were accompanied by recollective experience ('remember' responses) and which were recognized on some other basis ('know' responses). Our results showed that both the self-reference condition and mother condition were associated with the same highest proportion of correct remember responses and the same lowest proportion of correct know responses. In contrast, for Western subjects, the self-reference condition, relative to the mother condition, was associated with a higher proportion of correct remember responses and a lower proportion of correct know responses. We discussed the results with reference to the HERA model (hemispheric encoding/retrieval asymmetry).

The Resolution of the Great 20th Century Debate in the Foundations of Mathematics

The paper resolves the great debate of the 20th century between the three philosophies of mathematics-logicism, intuitionism and formalism—founded by Bertrand Russell and A. N. Whitehead, L. E. J. Brouwer and David Hilbert, respectively. The issue: which one provides firm foundations for mathematics? None of them won the debate. We make a critique of each, consolidate their contributions, rectify their weakness and add our own to resolve the debate. The resolution forms the new foundations of mathematics. Then we apply the new foundations to assess the status of Hilbert’s 23 problems most of which in foundations and find out which ones have been solved, which ones have flawed solutions that we rectify and which ones are open problems. Problem 6 of Hilbert’s problems—Can physics be axiomatized?—is answered yes in E. E. Escultura, Nonlinear Analysis, A-Series: 69(2008), which provides the solution, namely, the grand unified theory (GUT). We also point to the resolution of the 379-year-old Fermat’s conjecture (popularly known as Fermat’s last theorem) in E. E. Escultura, Exact Solutions of Fermat’s Equations (Definitive Resolution of Fermat’s Last Theorem), Nonlinear Studies, 5(2), (1998). Likewise, the proof of the 274-year-old Goldbach’s conjecture is in E. E. Escultura, The New Mathematics and Physics, Applied Mathematics and Computation, 138(1), 2003.

Photonic spin Hall effect and terahertz gas sensor via InSb-supported long-range surface plasmon resonance

We propose a simple one-dimensional grating coupling system that can excite multiple surface plasmon resonances for refractive index(RI)sensing with self-reference characteristics in the near-infrared band.Using theoretical analysis and the finite-difference time-domain method,the plasmonic mechanism of the structure is discussed in detail.The results show that the excited resonances are independent of each other and have different fields of action.The mode involving extensive interaction with the analyte environment achieves a high sensitivity of 1236 nm/RIU,and the figure of merit(FOM)can reach 145 RIU-1.Importantly,the mode that is insensitive to the analyte environment exhibits good self-reference characteristics.Moreover,we discuss the case of exchanging the substrate material with the analyte environment.Promising simulation results show that this RI sensor can be widely deployed in unstable and complicated environments.

Systems Analysis in the Study of the Political Elite

The main topic of the research is applying of systems approach in studying of political elite. This approach was applied in the analysis of Russia＇s regional power elite （1991 to 2010）. The elite was studied as a complex self-reference system oriented at its own environment, not only in an adaptive way, but first and foremost in structure. The systems approach specifies the following conceptual framework of the study： self-reference, system boundaries, and interaction between the political elite and the surrounding world. Application of the systems analysis to studying the political elite enabled to analyze the structure and functions of the elite, create a model of elitogenesis, and receive study matrix.

The Constructivist Real Number System

The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundations of mathematics. The critique of the traditional foundations of mathematics reveals a number of errors including inconsistency (contradiction or paradox) and undefined and vacuous concepts which fall under ambiguity. Critique of the real and complex number systems reveals similar defects all of which are responsible not only for the unsolved long standing problems of foundations but also of traditional mathematics such as the 379-year-old Fermat’s last theorem (FLT) and 274-year-old Goldbach’s conjecture. These two problems require rectification of these defects before they can be resolved. One of the major defects is the inconsistency of the field axioms of the real number system with the construction of a counterexample to the trichotomy axiom that proved it and the real number system false and at the same time not linearly ordered. Indeed, the rectification yields the new foundations of mathematics, constructivist real number system and complex vector plane the last mathematical space being the rectification of the complex real number system. FLT is resolved by a counterexample that proves it false and the Goldbach’s conjecture has been proved both in the constructivist real number system and the new real number system. The latter gives to two mathematical structures or tools—generalized integral and generalized physical fractal. The rectification of foundations yields the resolution of problem 1 and the solution of problem 6 of Hilbert’s 23 problems.

Hilbert＇s Foundations Remain Intact

Some of the seemingly important contributions made by Russell, Cantor and Godel regarding the foundations of mathematics lose credibility when addressed at a more fundamental level which assumes language consists of symbols devoid of what they mean. Such an approach can reveal neglected assumptions which are of consequence when made explicit and which, in particular, mean that Hilbert in fact had no need to heed Godel＇s revolutionary results regarding the foundations of mathematics.

In search of the Chinese self:An fMRI study

Cultural influences on the concept of self is a very important topic for social cognitive neuroscientific exploration, as yet, little if anything is known about this topic at the neural level. The present study investigates this problem by looking at the Chinese culture’s influence on the concept of self, in which the self includes mother. In Western cultures, self-referential processing leads to a memory performance advantage over other forms of semantic processing including mother-referential, other-referential and general semantic processing, and an advantage that is potentially localizable to the medial prefrontal cortex (MPFC). In Chinese culture, however, the behavioral study showed that mother-referential processing was comparable with self-referential processing in both memory per-formance and autonoetic awareness. The present study attempts to address whether similar neural correlates (e.g. MPFC) are acting to facilitate both types of referencing. Participants judged trait ad-jectives under three reference conditions of self, other and semantic processing in Experiment I, and a mother-reference condition replaced the other-reference condition in Experiment II. The results showed that when compared to other, self-referential processing yielded activations of MPFC and cingulate areas. However, when compared to mother, the activation of MPFC disappeared in self-referential processing, which suggests that mother and self may have a common brain region in the MPFC and that the Chinese idea of self includes mother.