Pixel’s Quantum Image Enhancement Using Quantum Calculus

The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values.The technique focuses on boosting the edges and texture of an image while leaving the smooth areas alone.The brain Magnetic Resonance Imaging(MRI)scans are used to visualize the tumors that have spread throughout the brain in order to gain a better understanding of the stage of brain cancer.Accurately detecting brain cancer is a complex challenge that the medical system faces when diagnosing the disease.To solve this issue,this research offers a quantum calculus-based MRI image enhancement as a pre-processing step for brain cancer diagnosis.The proposed image enhancement approach improves images with low gray level changes by estimating the pixel’s quantum probability.The suggested image enhancement technique is demonstrated to be robust and resistant to major quality changes on a variety ofMRIscan datasets of variable quality.ForMRI scans,the BRISQUE“blind/referenceless image spatial quality evaluator”and the NIQE“natural image quality evaluator”measures were 39.38 and 3.58,respectively.The proposed image enhancement model,according to the data,produces the best image quality ratings,and it may be able to aid medical experts in the diagnosis process.The experimental results were achieved using a publicly available collection of MRI scans.

A Vector Tensor Calculus Description of a Euclidean Space

We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity argument.We then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1) by showing that the linearized operator is a contraction mapping under the right circumstances.

Using laparoscope to remove an ectopic intrauterine device in the anterior wall of urinary bladder:A case report

BACKGROUND An intrauterine device(IUD)is a contraceptive device placed in the uterine cavity and is a common contraceptive method for Chinese women.However,an IUD may cause complications due to placement time,intrauterine pressure and other factors.Ectopic IUDs are among the most serious complications.Ectopic IUDs are common in the myometrium and periuterine organs,and there are few reports of ectopic IUDs in the urinary bladder,especially in the anterior wall.CASE SUMMARY A 52-year-old woman was hospitalized due to a urinary bladder foreign body found via abdominal ultrasound and computed tomography(CT)examination.The patient had a 2-year history of recurrent abdominal distension and lower abdominal pain,accompanied by frequent urination,urgency,dysuria and other discomfort.Ultrasound examination revealed foreign bodies in the bladder cavity,with calculus on the surface of the foreign bodies.CT revealed a circular foreign body on the anterior wall of the urinary bladder,suggesting the possibility of an ectopic IUD.After laparoscopic exploration,an annular IUD was found in the anterior wall of urinary bladder,and an oval calculus with a diameter of approximately 2 cm was attached to the surface of the bladder cavity.The IUD and calculus were successfully and completely removed.The patient recovered well after surgery.CONCLUSION Abdominal ultrasound and CT are effective methods for detecting ectopic IUDs.The IUD is located in the urinary bladder and requires early surgical treatment.The choice of surgical method is determined by comprehensively considering the depth of the IUD in the bladder muscle layer,the situation of complicated calculus,the situation of intravesical inflammation and medical technology and equipment.

Fault Diagnosis Method of Rolling Bearing Based on ESGMD-CC and AFSA-ELM

Incomplete fault signal characteristics and ease of noise contamination are issues with the current rolling bearing early fault diagnostic methods,making it challenging to ensure the fault diagnosis accuracy and reliability.A novel approach integrating enhanced Symplectic geometry mode decomposition with cosine difference limitation and calculus operator(ESGMD-CC)and artificial fish swarm algorithm(AFSA)optimized extreme learning machine(ELM)is proposed in this paper to enhance the extraction capability of fault features and thus improve the accuracy of fault diagnosis.Firstly,SGMD decomposes the raw vibration signal into multiple Symplectic geometry components(SGCs).Secondly,the iterations are reset by the cosine difference limitation to effectively separate the redundant components from the representative components.Additionally,the calculus operator is performed to strengthen weak fault features and make them easier to extract,and the singular value decomposition(SVD)weighted by power spectrum entropy(PSE)can be utilized as the sample feature representation.Finally,AFSA iteratively optimized ELM is adopted as the optimized classifier for fault identification.The superior performance of the proposed method has been validated by various experiments.

Variational Approach to Heat Conduction Modeling

It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.

The Absence of “Perfect Induction”in the Science

The present paper is finalized to show that the Science, even if considered in its two different Phenomenological Approaches at present known, is unable to assert that: “Thinks are like that”. This is because both the two Scientific Approaches previously mentioned have not the property of “the perfect induction”. Consequently, although they can even reach an experimental confirmation of the theoretical results, and thus a “valid description” of the various phenomena of the surrounding world, such a description has not an “absolute value”. In fact, it always and only has an “operative validity”, that is, it exclusively and solely refers to an “experimental point of view”. This means that such an “operative validity” cannot represent the basis for a logical process characterized by a “perfect induction”. In addition, the Traditional Scientific Approach is also characterized by “Insoluble” Problems, “Intractable Problems”, Problems with “drifts”, which could generally be termed as “side effects”. On the other hand, the same com-possible Scientific Approach based on the Emerging Quality of Self-Organizing Systems, also presents its “Emerging Exits”. Consequently, none of the two mentioned scientific Approaches has the “gift” of “the perfect induction”. However, there are significant differences between the two. Differences that may “suggest” the most appropriate choice among them for an “operative point of view”. This conclusion will be com-proved by considering, with particular reference, both the “side effects”, which are related to the Traditional Approach and, on the other hand, the “Emerging Exits”, which specifically pertain to the new Scientific Approach based on the Emerging Quality of Self-Organizing Systems.

Elements of Electromagnetic Matter

Originally, Maxwell attempted to express his electromagnetic theory using four-dimensional mathematics of quaternions. Maxwell’s equations were later re-written in a three-dimensional real vector form, which is how the theory is presented today. Thus, an interesting question remains whether we can derive electromagnetic equations analytically from the basic mathematical principles of quaternion algebra and calculus, resulting in general and analytic matter equations. This question seems highly intriguing. Previously, we developed a mathematical theory of time using a normed division algebra of real quaternions [1]. In this study, we extend the theory of time by presenting a new analytical derivation of electromagnetic matter equations using the calculus of real quaternions, as originally intended by Maxwell. Therefore, we propose a novel mathematical definition of the quaternion path derivative using the properties of quaternion division. We then apply the quaternion derivative to an external electromagnetic potential and assume that the first quaternion derivative represents the quaternion electromagnetic force. Next, we assume that the second derivative, or quaternion Laplacian operator, applied to an external electromagnetic potential leads to the quaternion electromagnetic current density. The new analytical expressions are similar to the original empirical Maxwell equations, except for an additional scalar electric field, which allows for a novel formulation of Ohm’s conductivity law. We demonstrate that the resulting analytical equations can be written equivalently using either electromagnetic potentials or fields. Finally, we summarize the key postulates and equations of the new electromagnetic matter theory, which were based on normed division algebra and the calculus of quaternions. The resulting theory appears to be a useful analytical enhancement of the original Maxwell equations, and therefore, seems highly comprehensive, logical, and compelling.

The Accelerated Expansion of the Universe in the Light of the Maximum Ordinality Principle

The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.

Variational Approach to 2D and 3D Heat Conduction Modeling

The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.

一本有新意的微积分教材——评美国MIT教授Strang新编《CALCULUS》

微积分教材数以千计,每年都有不少新作问世,但有新意者却如凤毛麟角。91年夏我到美国参加第二届国际工业与应用数学大会(ICIAM’91),在大会展厅看到美国麻省理工学院(MIT)数学系教授、美国工业与应用数学学会(SIAM)教育委员会主席Strang教授刚刚出版的《CALCULUS》,很有特色,会后应邀访问MIT。

基于Pi-Calculus的跨组织工作流建模方法

针对跨组织协同环境下的业务流程建模技术的不足,提出了一个新的用于跨组织业务流程的形式化建模方法。首先根据工作流管理联盟(W fMC)的有关工作流过程定义接口规范,利用Pi-Calculus技术对跨组织业务流程结构进行了形式化定义。此外,利用Pi-Calculus特有机制对并发流程及其之间的通信进行描述。提出的方法可以有效用于不同业务流程间的协同工作,并且适合于对分布式协同环境下的工作流进行建模。

Effects of in vitro cultivated Calculus Bovis compound on pulmonary lesions in rabbits with schistosomiasis

AIM:To explore the interventional effects and mechanism of in vitro cultivated Calculus Bovis compound preparation(ICCBco) on pulmonary lesions in portal hypertensive rabbits with schistosomiasis. METHODS:The experimental group included 20 portal hypertensive rabbits with schistosomiasis treated by ICCBco.The control group included 20 portal hypertensive rabbits with schistosomiasis treated by praziquantel. The morphological changes of the pulmonary tissues were observed under light and electron microscopy.The expression of fibronectin(FN) and laminin(LN) in the lung tissues was analyzed by immunohistochemistry. RESULTS:Under light microscope,the alveolar exudation in the lung tissue was more frequently observed in the control group,while the alveolar space was fairly dry in the lung tissue of ICCBco group.Under electron microscope,more alveolar exudation in the lung tissue,and moremacrophages,alveolar angiotelectasis and the blurred three-tier structure of alveolar-capillary barrier could be seen in the control group.In ICCBco group,fibers within the alveolar interspace slightly increased in some lung regions,and the structure of typeⅠepithelium,basement membrane and endodermis was complete,and no obvious exudation from the alveolar space,and novascular congestion could be observed.There was a positive or strong positive expression of FN and LN in the lung tissue of the control group,while there was a negative or weak positive expression of FN and LN in ICCBco group. CONCLUSION:ICCBco can effectively prevent pulmonary complications in portal hypertensive rabbits with schistosomiasis by means of improving lung microcirculation and lowering the content of extracellular matrix.

Performance Evaluation for SDN Deployment: an Approach Based on Stochastic Network Calculus

The Open Flow implementations(SDNs) have been deployed increasingly on varieties of networks in research institutions as well as commercial institutions. To develop an Open Flow implementation, it is required to understand the performance of the network. A few benchmark tools(e.g., Cbench and OFlops) can be used to measure the network performance, while these tools take considerable time to simulate traffic behaviors and generate the required results,therefore extending the development time. In this paper, we present an analytical model, which is based on stochastic network calculus theory, for evaluating the performance of switch to controller.The previous studies show that stochastic network calculus can provide realistic emulation of real network traffic behaviors. Our model is evaluated by using both simulation tool and realistic testbed.The results show the stochastic network calculus based analysis model can realistically measure the network performance of the end-to-end properties between controller and switch.

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of fac- tional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential consider- ing particle breakage is used. Test results of several types of granular soils are used to validate the model performance.

CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS

The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.

ON THE FRACTIONAL CALCULUS FUNCTIONS OF A FRACTAL FUNCTION

Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.

Robust Attitude Control for Reusable Launch Vehicles Based on Fractional Calculus and Pigeon-inspired Optimization

In this paper, a robust attitude control system based on fractional order sliding mode control and dynamic inversion approach is presented for the reusable launch vehicle(RLV)during the reentry phase. By introducing the fractional order sliding surface to replace the integer order one, we design robust outer loop controller to compensate the error introduced by inner loop controller designed by dynamic inversion approach. To take the uncertainties of aerodynamic parameters into account,stochastic robustness design approach based on the Monte Carlo simulation and Pigeon-inspired optimization is established to increase the robustness of the controller. Some simulation results are given out which indicate the reliability and effectiveness of the attitude control system.

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

Network Calculus在机载雷达设计中的应用

Network Calculus是一种基于最小加代数理论来分析网络数据流的方法,它已被广泛应用于工业、航空和航天的复杂网络设计中。机载雷达要求系统具有高实时性,尤其对嵌入式任务的调度有严格的时序要求。在机载雷达的设计中应用此理论,可以在系统前期设计时提供实时性的理论依据和保障,为雷达系统的实时性设计提供了一种方法和手段。