The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones

The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.

Dilation,discrimination and Uhlmann's theorem of link products of quantum channels

We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

Perception of fundamental science to boost lithium metal anodes toward practical application

As a key material for lithium metal batteries(LMBs),lithium metal is one of the most promising anode materials to break the bottleneck of battery energy density and a commonly used active material for reference electrodes.Although lithium anodes are regarded as the holy grail of lithium batteries,decades of exploration have not led to the successful commercialization of LMBs,due mainly to the challenges related to the inherent properties of lithium metal.To pave the way for further investigation,herein,a comprehensive review focusing on the fundamental science of lithium are provided.Firstly,the natures of lithium atoms and their isotopes,lithium clusters and lithium crystals are revisited,especially their structural and energetic properties.Subsequently,the electrochemical properties of lithium metal are reviewed.Numerous important concepts and scientific questions,including the electronic structure of lithium,influence of high pressure and low temperature on the properties of lithium,factors influencing lithium deposition,generation of lithium dendrites,and electrode potential of lithium in different electrolytes,are explained and analyzed in detail.Approaches to improve the performance of lithium anodes and thoughtfulness about the electrode potential in lithium battery research are proposed.

New Asymptotic Results on Fermat-Wiles Theorem

We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.

Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials

Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

New Approach to Synchronize General Relativity and Quantum Mechanics with Constant “K”-Resulting Dark Matter as a New Fundamental Force Particle

Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “αs” for that fundamental force is 1.08 × 10-23. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.

Performance in the Fundamentals of Laparoscopic Surgery: Does it reflect global rating scales in the Objective Structured Assessment of Technical Skills in porcine laparoscopic surgery?

Objective:To correlate the utility of the Fundamentals of Laparoscopic Surgery(FLS)manual skills program with the Objective Structured Assessment of Technical Skills(OSATS)global rating scale in evaluating operative performance.Methods:The Asian Urological Surgery Training and Educational Group(AUSTEG)Laparoscopic Upper Tract Surgery Course implemented and validated the FLS program for its usage in laparoscopic surgical training.Delegates’basic laparoscopic skills were assessed using three different training models(peg transfer,precision cutting,and intra-corporeal suturing).They also performed live porcine laparoscopic surgery at the same workshop.Live surgery skills were assessed by blinded faculty using the OSATS rating scale.Results:From March 2016 to March 2019,a total of 81 certified urologists participated in the course,with a median of 5 years of post-residency experience.Although differences in task time did not reach statistical significance,those with more surgical experience were visibly faster at completing the peg transfer and intra-corporeal suturing FLS tasks.However,they took longer to complete the precision cutting task than participants with less experience.Overall OSATS scores correlated weakly with all three FLS tasks(peg transfer time:r=0.331,r^(2)=0.110;precision cutting time:r=0.240,r^(2)=0.058;suturing with intracorporeal knot time:r=0.451,r^(2)=0.203).Conclusion:FLS task parameters did not correlate strongly with OSATS globing rating scale performance.Although FLS task models demonstrated strong validity,it is important to assimilate the inconsistencies when benchmarking technical proficiency against real-life operative competence,as evaluated by FLS and OSATS,respectively.

Fundamental Principles behind Climate Change

The attribution of climate change is complex,and the current mainstream view is more inclined towards human activities and carbon dioxide emissions from fossil fuels.Any complex problem is composed of basic principles.This article elaborates on the basic logic behind climate change(a global hot topic)through basic principles such as reaction types,carbon thermal properties of biomass energy,greenhouse gas attribution,ecological basic theory,and energy cycle.

Small Modular Solutions to Fermat’s Last Theorem

The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.

The Intervention Path of Fundamental Rights under the Scope of International Private Law

In recent years, international private law scholars have argued for the radiating effect of fundamental rights on international private law by introducing constitutional theory. However,there remains a lack of systematic research on how fundamental rights should be integrated into judicial practices concerning foreign-related civil and commercial cases. Throughout the development of international private law, public policy has served as a historical carrier of substantive values for judicial entities and has consistently played a crucial role in value review. In cases of international private law where conflicts arise with the values of fundamental rights, public policy indirectly excludes the legal choice outcomes to safeguard the human rights values inherent in fundamental rights from infringement.However, due to limitations imposed by the degree of connection and relative conditions, traditional paths of public policy have certain constraints and cannot provide comprehensive protection for fundamental rights. Therefore, there is a need for judges to shift their logical paradigms, transcend bilateral choice-of-law models, and introduce a direct intervention path for fundamental rights. This direct intervention path utilizes the logical analysis framework of the protection scope,intervention, and justification of fundamental rights. It can effectively balance conflicting legal interests and maximize the protection of the fundamental rights of the parties involved.

Frame Length Dependency for Fundamental Frequency Extraction in Noisy Speech

The fundamental frequency plays a significant part in understanding and perceiving the pitch of a sound. The pitch is a fundamental attribute employed in numerous speech-related works. For fundamental frequency extraction, several algorithms have been developed which one to use relies on the signal’s characteristics and the surrounding noise. Thus, the algorithm’s noise resistance becomes more critical than ever for precise fundamental frequency estimation. Nonetheless, numerous state-of-the-art algorithms face struggles in achieving satisfying outcomes when confronted with speech recordings that are noisy with low signal-to-noise ratio (SNR) values. Also, most of the recent techniques utilize different frame lengths for pitch extraction. From this point of view, This research considers different frame lengths on male and female speech signals for fundamental frequency extraction. Also, analyze the frame length dependency on the speech signal analytically to understand which frame length is more suitable and effective for male and female speech signals specifically. For the validation of our idea, we have utilized the conventional autocorrelation function (ACF), and state-of-the-art method BaNa. This study puts out a potent idea that will work better for speech processing applications in noisy speech. From experimental results, the proposed idea represents which frame length is more appropriate for male and female speech signals in noisy environments.

Seismology in the Light of Fundamental Sciences

According to the definition, seismology is a science that studies the processes and causes of seismic phenomena and the structure of the Earth, i.e. a scientific discipline that studies the movement of blocks of rocks of the Earth’s crust and mantle and related phenomena. Seismology conducts research in the following areas and is designed to scientifically explain two main issues: 1) Study of the nature of seismic phenomena and the internal structure of the Earth. Why, how and where do seismic impacts occur? 2) Protecting humanity from the catastrophic consequences of seismic events. Is it possible to predict seismic impacts? Like any other scientific discipline, seismology is obliged to follow the laws of science and its fundamental principles. This article is devoted to the description of violations of the fundamental laws of science committed by seismologists in the study of seismic processes and raises the question of compliance of the stated research directions with the current level of development of sciences. Answering point No. 1, regarding the structure of the Earth, it is possible to recognize some successes of seismology, which nevertheless cause great doubts in the scientific community of geophysicists, because if the stratigraphic data of ultra-deep wells often refute [1] the conclusions made by seismologists on the structure of the Earth’s crust at shallow depth, then to assert something unambiguously about the structure of the mantle and at the present stage, seismology cannot. Answering the main questions of seismology, why seismic phenomena occur, and how earthquake energy is formed, seismologists have not had, and have not. Answering point No. 2, we can confidently say that in the matter of forecasting seismic phenomena, seismology has not advanced one iota over the past century, and as seismologists have been confused in the search for earthquake prediction algorithms, they are also confused without any hope of success. All that modern seismology can “boast” is the theory of Elastic recoil [2], the absurdity of which does not cause any doubt among the progressive part of geophysicists. But, the fact that most of the leading scientists-seismologists continue to piously believe the conclusions of the Elastic Recoil theory puts seismology in a humiliating position, because Mr. Reid’s theory is the clearest example of a false theory based on scientific incompetence of scientists, a model of brazen violation of the fundamental laws of science and the foundation of false and ignorant conclusions. Based on the results achieved, or rather on their absence, we regret to draw a sad conclusion: modern seismology is in the deepest decline, the cause of which is the incompetence of researchers as a result of their catastrophically low level of academic training, who stuff the scientific community with scientific geophysical rubbish, breeding similar ignoramuses in seismology. We understand that by asserting this, we offend most seismologists, but it is impossible to continue to tolerate this state of affairs in geophysics, because: “Amicus plato, sed magis amica est veritas.” Obviously, the time has come for a new meteorologist, Alfred Wagener [3], who will come and teach seismologists not to guess on coffee grounds, but to investigate seismic processes using the fundamental laws of science. In this article, we not only investigate the reasons for the unsatisfactory state of affairs in seismology, but also give our answers to the questions, of why earthquakes occur and how seismic energy is formed.

Whole Perfect Vectors and Fermat’s Last Theorem

A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.

Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

Effect of simulating training of the fundamentals of laparoscopic surgery on the attitude of operating room nurses students:an intervention study

Objective:Clinical education plays a key role in preparing students for patient care.Laparoscopy is one of the most important minimally invasive surgeries(MISs)wherein surgical technologists are responsible for camera navigation and assistant surgeons are responsible for peg transfer.Therefore,it is necessary to improve the attitude of the operating room students toward these skills during their study period.The present study was conducted to determine the effect of simulating training in the fundamentals of laparoscopic surgery(FLS)on the attitude of the operating room students.Methods:This interventional study was conducted on 28 operating room students of Iran University of Medical Sciences in 2019.The census sampling method was used.The data-collection tool included the“Intrinsic motivation inventory(IMI)questionnaire.”The educational intervention was carried out in theoretical(booklet design)and practical(simulation)sections.Data analysis was carried out using descriptive and inferential analyses including the paired t-test,Mann–Whitney U test,and independent t-test.The collected data were analyzed using R and SPSS software.P-value<0.05 was considered as the significant level.Results:The mean±SD of the participants'age was 22.93±2.14 years,and the majority of them were women(67.9%).There was a significant difference in the mean scores of students'attitudes toward the FLS before and after the educational intervention(P<0.001)in all dimensions(interest,perceived competence,perceived choice,and tension).There was also a significant correlation between gender and interest dimension(P=0.005).Conclusions:The results of the present study showed that simulating the training FLS curriculum positively affects students'attitudes.Therefore,the researchers suggest that for creating a positive attitude,increasing students'interest in laparoscopic surgery,and ensuring a more effective presence in the operating room,this training should be considered in the operating room curriculum.

A Study on High School Mathematics Teaching Design Based on Teaching for Robust Understanding: Taking the Cosine Theorem as an Example

Teachers’teaching behavior plays a crucial role in students’development,and there are problems in the current teaching behavior of mathematics teachers such as ignoring students’cognitive needs,lack of equal opportunities for students’classroom performance as well as lack of formative evaluation of students.In order to solve the phenomenon,this paper analyzes and explains how to promote teaching based on the Teaching for Robust Understanding(TRU)evaluation framework with the goal of focusing on the development of all students,taking the teaching design of The Cosine Theorem as an example,and provides ideas and methods for first-line high school mathematics teachers.

On Some Fundamental Theorems in Stability Theory

This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.