Principal Part Research Articles

On weak solution of SDE driven by inhomogeneous singular Lévy noise

We study a time-inhomogeneous SDE in R d \mathbb {R}^d driven by a cylindrical Lévy process with independent coordinates which may have different scaling properties. Such a structure of the driving noise makes it strongly spatially inhomogeneous and complicates the analysis of the model significantly. We prove that the weak solution to the SDE is uniquely defined, is Markov, and has the strong Feller property. The heat kernel of the process is presented as a combination of an explicit ‘principal part’ and a ‘residual part’, subject to certain L ∞ ( d x ) ⊗ L 1 ( d y ) L^\infty (dx)\otimes L^1(dy) and L ∞ ( d x ) ⊗ L ∞ ( d y ) L^\infty (dx)\otimes L^\infty (dy) -estimates showing that this part is negligible in a short time, in a sense. The main tool of the construction is the analytic parametrix method, specially adapted to Lévy-type generators with strong spatial inhomogeneities.

Sensor Fault Diagnosis Using a Machine Fuzzy Lyapunov-Based Computed Ratio Algorithm.

Anomaly identification for internal combustion engine (ICE) sensors has become an important research area in recent years. In this work, a proposed indirect fuzzy Lyapunov-based computed ratio observer integrated with a support vector machine (SVM) was designed for sensor fault classification. The proposed fuzzy Lyapunov-based computed ratio observer integrated with SVM has three main layers. In the preprocessing (first) layer, the resampled root mean square (RMS) signals are extracted from the original signals to the designed indirect observer. The second (observation) layer is the principal part with the proposed indirect fuzzy sensor-fault-classification technique. This layer has two sub-layers: signal modeling and estimation. The Gaussian autoregressive-Laguerre approach integrated with the fuzzy approach is designed for resampled RMS fuel-to-air-ratio normal signal modeling, while the subsequent sub-layer is used for resampled RMS fuel-to-air-ratio signal estimation using the proposed fuzzy Lyapunov-based computed ratio observer. The third layer, for residual signal generation and classification, is used to identify ICE sensor anomalies, where residual signals are generated by the difference between the original and estimated resampled RMS fuel-to-air-ratio signals. Moreover, SVM is suggested for residual signal classification. To test the effectiveness of the proposed method, the results are compared with two approaches: a Lyapunov-based computed ratio observer and a computed ratio observer. The results show that the accuracy of sensor anomaly classification by the proposed fuzzy Lyapunov-based computed ratio observer is 98.17%. Furthermore, the proposed scheme improves the accuracy of sensor fault classification by 8.37%, 2.17%, 6.17%, 4.57%, and 5.37% compared to other existing methods such as the computed ratio observer, the Lyapunov-based computed ratio observer, fuzzy feedback linearization observation, self-tuning fuzzy robust multi-integral observer, and Kalman filter technique, respectively.

Is the Report of Lazarus's Death Premature? A Reply yo Cameron and Postlewaite

Over a year ago, Ms. Faith Cuenin and I wrote an article in this Review (which I hereafter refer to as the “2004 Article”) about the tax treatment of guaranteed payments under section 707(c) that are made in kind. We concluded that a partnership does not recognize gain or loss on the making of a guaranteed payment with appreciated or depreciated property. We also concluded that the partner’s basis in the property received will equal its fair market value at the time of payment, and that the payment does not affect the partner’s outside basis in his partnership interest except to the extent of the partner’s share of any deduction that the partnership obtained by making the payment. Professors Cameron and Postlewaite strongly disagree with one of the conclusions we reached in our Article (i.e., our conclusion that the partnership does not recognize gain or loss) and with all of our reasoning. They are publishing in this issue of the Florida Tax Review (in what I will refer to as their “Lazarus Effect” Article) their analysis for rejecting our treatment of the topic. While I find their arguments well reasoned and documented, for reasons that I will explain in this response, I continue to hold to the conclusions that Ms. Cuenin and I reached in the 2004 Article. I will not reiterate in this response all of the analysis that is set forth in the 2004 Article, and I hope that an interested reader will turn to that piece. I will, however, respond to many of the points that are made in Cameron and Postlewaite’s Lazarus Effect Article.The Lazarus Effect Article can be divided into two principal parts. One is the contention that section 707(c) was impliedly or effectively repealed by the adoption of section 707(a)(2) as part of the Tax Reform Act of 1984.3 The second is a contention that, even if section 707(c) is still viable, the conclusion concerning the partnership’s nonrecognition of income that Ms. Cuenin and I reached in the 2004 Article, and our reasons for reaching that conclusion, are wrong. I will address both contentions.

Indigenous Knowledge of Medicinal Plants to Treat Human Illness in Gimbo and Didessa Districts in the Southwest of Ethiopia

ABSTRACT This study aimed to gather and document information on medicinal plants used in Ethiopia using an ethnomedicinal survey. The survey identified 80 species of medicinal plants belonging to 39 botanical families by indigenous people in Gimbo and Didessa districts in the Southwest of Ethiopia for the treatment of 46 illnesses. The majority of medicinal plants used were herbs. Leaves were the principal part of the plant used for the preparation of herbal remedies and formulations. Most of the medicinal plants were obtained from the wild. The oral route was the most commonly used mode of administration of herbal medicine. Water and salt were the most frequently used excipients for the preparation of herbal remedies. Croton macrostachyus, Clerodendrum myricoides, Ocimun laminafollum, Phytolacca dodecandra, and Vernonia amygdalina were the most repeatedly claimed medicinal plants by the informants.

US APR vs EU APR, and the Substitute Tax on Loan Effects on These Formulas

In Italy, especially these days, we have been dealing with the common “mortgage constant”, technically built under the principles of the compounded interest methods. This worldwide well-known financial technique clearly shows that every single rate is constant and composed by the sum of the principal part + the accrued interest. The rates of this kind of amortization plan result in an inversely proportional scheme: higher interest reimbursed at the beginning of the amortization plan, increasing rate by rate. If this is unquestionable everywhere, the Italian Courts and many Italian banks officially deny that this amortization plan technique incorporates compound interest and anatocism, although the mortgage constant is on the compounded interest structure, as per the anatocism effect in it. In order to defend this thesis about the absence of anatocism in compounded interest on constant rate, basically, all the other Senior Expert Witnesses of the Italian Courts recall EU APR formula, constantly declaring that it is equal to IRR formula, without any differences, without any exceptions. Their statement, confirmed by many Italian Courts, is that EU APR formula is exactly corresponding to the IRR formula, determined using the IRR Excel function (XIRR). My study states that this is very incorrect, that the IRR formula (and function) is equal to the US APR, which assume as an APY, and different from EU APR, better to define as EAR.

Corrected Internal Torques of Gyroscopic Effects

The dynamics of the rotating objects is the complex piece of the classical mechanics which example presented by gyroscopic effects. Researchers study gyroscope problems during the centuries and obtained not comforting analytical results. The physics of gyroscopic effects does not have an adequate description. The recent investigation finally solved the gyroscope problems in principle but some mathematical models for gyroscopic inertial torques contained mechanical errors. The corrected gyroscope theory opened breakthrough directions in the solutions to dynamics of rotating objects. This publication presents a summation of the gyroscope theory that gives a general presentation of its principal parts.

Time-asymptotic stability for first-order symmetric hyperbolic systems of balance laws in dissipative compressible fluid dynamics

This paper identifies a non-(or /iso-)thermal variant of Ruggeri’s 1983 formulation of viscous heat-conductive fluid dynamics as a hyperbolic system of balance laws and shows that both the original model and this variant have (a) time-asymptotically stable equilibria and (b) principal parts deriving from a protopotential: a single scalar function that induces the temporospatial flux as an appropriate part of its Hessian.

Inhomogeneous wave equation with t-dependent singular coefficients

This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are formulated in order to obtain a very weak solution as introduced in [15]. Very weak solutions for this kind of equations are also investigated from a numerical point of view in two toy models: the wave equation with a Heaviside function and a delta distribution, respectively, as coefficient in its principal part.

Evolution paths of green economy modes and their trend of hypercycle economy

So far there is a lack of specialized research on the entire path and the law of the evolution of green economy modes, especially studies on its future trend. Some studies have been done only on its sub-process, in which there are some shortcomings such as overlapping and incomplete classification of economy modes, as well as the lack of mechanism models to describe the modes. This paper attempts to solve those problems. Firstly, various green economy modes are extracted and classified, and then their evolution paths are identified and reviewed, according to sustainable development theory, hypercycle theory, etc., and to practical investigation. Secondly, theoretical models for each green economy mode and their multilevel dynamic evolution models in a practical field (forestry as an example) are established by the modeling method of system structure. Finally, the evolution law of green economy mode is analyzed systematically by means of the above-mentioned models. According to the research, some conclusions are drawn as follows: First, green economy modes have evolved through three stages as a whole. The first is the start-up stage, in which the mode is the ‘from cradle to grave’ end-treatment green economy (GE-I). The second is the growth stage, in which the mode is the ‘from cradle to cradle’ resources-chain closed-loop green economy (GE-Ⅱ). The third is the mature stage, in which the mode will be the ‘from breeding to breeding ‘three-chain hypercycle economy (GE-Ⅲ). Second, GE-Ⅱ has evolved through a specific process. In depth, the basic framework of GE-Ⅱ is based on the circular economy theory; and then it is combined gradually with some other relevant theories and technologies that are cleaner production, low-carbon economy and sharing economy and so on. In breadth, GE-Ⅱ is expanded layer by layer from unified enterprise GE-Ⅱ to diversified enterprise ( or cluster) GE-Ⅱ, and to societal GE-Ⅱ. The operational principle of GE-Ⅱ can be described by 3R theoretical model that includes 3 subsystems of reduction, recycle and reuse (3R), which are connected into an organic whole by resources chain. Third, GE-Ⅲ is evolving through a specific process of three-chain (3C) stage by stage expansion, from resources-chain primary hypercycle to eco-chain secondary hypercycle, and to value-chain tertiary hypercycle. The operational principle of GE-Ⅲ can be described by 5R-3C theoretical model that includes 5 subsystems of reduction, recycle, reuse, recultivation and reallocation (5R) , which are connected into an environment-economy self-organizing system by resources chain, ecochain and value chain. In the system, resources chain is the foundation, eco-chain is the support, and value chain is the impetus. The 3C hypercycle promotes and catalyze each other to realize mutualism between ecosystem and industrial system. Fourth, the related field of GE-Ⅲ includes the principal part of renewable-resource-based industry, and the expanded part of other relevant industries and even the whole society. Now in practice, GE-Ⅲ has initially formed. And in the future, it is the development tendency of green economy toward the establishment of the ecological civilization.

Assessment of the CHIVA and the ASVAL Method.

In this article, the CHIVA and ASVAL methods are assessed from the hemodynamic point of view. The CHIVA method comprises complicated, unusual terminology and new perceptions, such as closed and open shunts, fractionation of the hydrostatic pressure, subdivision of the venous network. The principal part of the CHIVA theory is the drainage of venous blood from the thigh saphenous system into the deep lower leg veins through the preserved saphenous trunk after high ligation at the saphenofemoral junction, which is considered as a beneficial, physiological phenomenon. In reality, this is recurrent reflux producing ambulatory venous hypertension. The main impact of the CHIVA procedure is the elimination of the saphenous reflux by high ligation at the saphenofemoral junction; thus it can be presumed that the CHIVA procedure yields similar results like the crossectomy. The ASVAL procedure is de facto the modification of the old Madelung method that was the prevalent surgical procedure before the Trendelenburg era in the 19th century. The results after ASVAL were not checked by plethysmography; there is a good case to suppose that the results after the ASVAL method would comply with those after sclerotherapy.

Weighted triplet loss based on deep neural networks for loop closure detection in VSLAM

Smart living is an emerging technology that has attracted a lot of attention all around the world. As a key technology of smart space, which is the principal part of smart living, the SLAM system has effectively expanded the ability of space intelligent robots to explore unknown environments. Loop closure detection is an important part of SLAM system and plays a very important role in eliminating cumulative errors. The SLAM system without loop closure detection is degraded to an odometer. The state estimation solely relying on an odometer will be seriously deviated in the long-term and large-scale navigation and positioning. This paper proposes a metric learning method that uses deep neural networks for loop closure detection based on triplet loss. The map points obtained by metric learning are fused with all map points in the current keyframe, and the map points that do not meet the filtering conditions are eliminated. Based on the Batch Hard Triplet loss, the weighted triplet loss function avoids suboptimal convergence in the learning process by applying weighted value constraints. At the same time, considering that fixed boundary parameters cannot be well adapted to the diversity of scales between different samples, we use the semantic similarity of anchor samples and negative samples to redefine boundary parameters. Finally, a SLAM system based on metric learning is constructed, and the SLAM dataset TUM and KITTI are used to evaluate the proposed model’s accuracy rate and recall rate. The scene features in this method are extracted automatically through neural networks instead of being artificially set. Finally, a high-precision closed-loop detection method based on weight adaptive triple loss is effectively realised through the closed-loop detection experiment. The minimum relative pose error is 0.00048 m, which is 15.8% less than that of the closed-loop detection algorithm based on the word bag model.

A brief introduction of Ayurvedic medical classics

Ayurveda can be traced back to 3000BC. It is the principal part of traditional medicine in India and other South Asian countries. It was divided into four historical periods according to the academic circle in India, ie. the Vedic period, the Samhita period, the Sangraha period and the modern period. The literature in the Vedic period mainly included Vedic Samhitas Brahmanas, Ramayana, Mahabharata. In the Samhita period, the "BrihatTrayee", namely, Caraka Samhita, Susruta Samhita and Astanga Hrdaya Samhita were published, indicating that Ayurveda had developed into a full-fledged medical system. In the Sangraha period, the "Laghu Trayee", namely, Madhava Nidana, Sarangadhara Samhita and Bhava Prakasa were published. At this time, a large number of annotated texts for these medical books emerged, which kept driving Ayurveda improvements. Since the modern period, Ayurvedic classical works were rearranged, edited and translated into different languages as cultural heritage, drawing attention worldwide. While the research to these works has been conducted widely in China, they are still short of systematic and professional translation and in-depth studies. This paper attempts to introduce the literature related to Ayurveda systematically, to pave the way for further research of Ayurvedic literature in the field of traditional Chinese medicine.

Resolvent and logarithmic residues of a singular operator pencil in Hilbert spaces

The present paper considers the operator pencil A(λ)=A0+A1λ, where A0,A1≠0 are bounded linear mappings between complex Hilbert spaces and A0 is neither one-to-one nor onto. Assuming that 0 is an isolated singularity of A(λ) and that the image of A0 is closed, certain operators are defined recursively starting from A0 and A1 and they are shown to provide a characterization of the image and null space of the operators in the principal part of the resolvent and of the logarithmic residues of A(λ) at 0. The relations with the classical results based on ascent and descent in [10] are discussed. In the special case of A0 being Fredholm of index 0, the present results characterize the rank of the operators in the principal part of the resolvent, the dimension of the subspaces that define the ascent and descent, the partial multiplicities, and the algebraic multiplicity of A(λ) at 0.

The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument.

Algebra of Borcherds products

Borcherds lift for an even lattice of signature ( p , q ) (p, q) is a lifting from weakly holomorphic modular forms of weight ( p − q ) / 2 (p-q)/2 for the Weil representation. We introduce a new product operation on the space of such modular forms and develop a basic theory. The product makes this space a finitely generated filtered associative algebra, without unit element and noncommutative in general. This is functorial with respect to embedding of lattices by the quasi-pullback. Moreover, the rational space of modular forms with rational principal part is closed under this product. In some examples with p = 2 p=2 , the multiplicative group of Borcherds products of integral weight forms a subring.

Bacillus spp. Contamination: A Novel Risk Originated From Animal Feed to Human Food Chains in South-Eastern Bangladesh.

The current study provides information on Bacillus spp. contamination along with present status in commercially available poultry and animal feeds as well as animal-derived products in Bangladesh. The research has been conducted to determine if animal feed and its components are a source of Bacillus spp. contamination in feed and food chain. Out of 180 different feeds, milk, egg, and human stool samples, 218 Bacillus spp. were isolated and identified by cultural morphology, microscopic, biochemical, and molecular characteristics where B. cereus, B. subtilis, B. amyloliquefaciens, B. licheniformis, B. thuringiensis, B. megaterium, and B. coagulans accounted for 51, 22, 9.1, 5.9, 5, 3.6, and 2.2%, respectively. Regarding the enumeration of total viable count and total Bacillus count, correspondingly 67 and 39% samples were found to be contaminated with above 10,000 CFU/g, while highest contamination was 85 and 75% in broiler feed, respectively. The total number of bacteria above the regulatory limits in commercially available feeds indicates a poor compliance with regulation and abuse administration in the Bangladeshi market. Moreover, a hospital-based survey showed that food-borne Bacillus spp. contributed to 4.5% human diarrhea cases and 25% food contamination associated with vegetables, rice, RTE food, milk, and egg, accounting for 46, 34, 14, 4, and 2%, respectively. B. cereus was the dominant isolate correspondingly accounting for 56 and 51% egg and milk contamination followed by B. amyloliquefaciens (32%) and B. thuringiensis (12%) in egg and B. subtilis (25%), B. amyloliquefaciens (12%), B. thuringiensis (6.4%), and B. coagulans (3.2%) in milk, respectively. Toxin gene profiling of Bacillus spp. revealed that B. cereus constituted a principal part of virulence, while B. thuringiensis, B. licheniformis, B. megaterium, B. coagulans, and B. subtilis showed genetic diversity and B. amyloliquefaciens had not carried any toxin gene. Detection rate of enterotoxin genes (nheA, nheB, nheC, cytK, hblA, hblC, hblD, and entFM) showed that 55% isolates carried nheABC genes, 80% entFM, and 71% cytK, whereas only 33% of the isolates contained hblACD gene clusters. These virulence genes were posing a threat to human health due to spread across the food and feed chain. Finally, our findings support the hypothesis that B. cereus might contribute to clinical diarrhea, gizzard erosion, and lung infection in duck and poultry, and that it contaminates animal-derived foods resulting in toxicity and antibacterial resistance to humans. Therefore, maximal tolerance limits of Bacillus spp. and their potential risks to the animal industry are urgently needed to clarify. Moreover, Bacillus spp.–induced toxin residual must be altered for human health via food chain transmission.

Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators

<p style='text-indent:20px;'>Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the Benjamin-Ono equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudo-differential operator of order 0 with principal part given by a modified Fourier transform (modification by a phase factor) and (2) the pullback of the Hamiltonian of the Benjamin-Ono is in normal form up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of para-differential operators. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the Benjamin-Ono equation under small, quasi-linear perturbations.</p>

IMPROVED INTELLIGENT BASE TECHNIQUE FOR PATH AND SOLUTION IN ROBOTIC USING PREWILL EDGE DETECTION PARADIGM

The major contribution in this research paper is concerned with the development of a humanoid robot using edge detection technique which selects features of the principal parts of the object and eliminates parts that are not necessary. The developed prototype of the motorized robot shows that robots in real life exhibit some level of intelligence. In the design process, the model of a humanoid robot was developed first using the simulink library tools in Matlab/Simulink environment. This research paper has improved autonomous path finding robots by incorporating very powerful and well-structured program/codes that gives the robot the ability to predict and make smart decision lending to efficient execution of desired assignment (picking of dirt in the surrounding).Result shows that the developed robot has simplified the way No robot interacts with object thereby saving cost and energy. A motorized autonomous path finding robot was designed and constructed to demonstrate the working principle of robot. The motorized robot and the humanoid robot have the capability to detect obstacle along its part at 30cm away from the obstacle. When the robot is switched on, it initializes after which forward movement until it gets 30cm closer to an obstacle it then stops, reverse backwards and then change direction. When it moves 30cm close to another obstacle, it stops reverse backwards, then turns left or right to another direction, and will continue to behave that way until the power button is switched off.

Performance Comparison between Lab-VIEW and MATLAB on Feature Matching-based Speech Recognition System

Speech recognition systems are widely used for smart applications. The smart application-based speech recognition system has different requirements for processing the human voice. The most common performance in the speech recognition system is essential to observe, since it is necessary to design smart application-based speech recognition systems for people's needs. Moreover, feature matching is the principal part of speech recognition systems since it plays a key role to authenticate, separate one human voice from another, and their different articulation. Therefore, this work proposes a performance comparison of speech recognition systems based on feature matching using Lab-VIEW and MATLAB. The feature extraction involves calculation of Mel Frequency Cepstral Coefficients (MFCC) for each frame. For the matching process, the system was tested 100 times for each five speeches by making changes in articulation with the same vocal cords. This matching process uses DTW (Dynamic Time Warping), and then the testing is based on the most common performance in the speech recognition system’s comparison between Lab-VIEW and MATLAB such as accuracy rate, execution time, and CPU usage. Based on experimental results, the average accuracy rate of MATLAB is better than Lab-VIEW. The execution time testing indicates that Lab-VIEW has a shorter execution time than MATLAB. On the other hand, Lab-VIEW and MATLAB have almost the same CPU usage. This result indicates that the performance comparison is able to be used according to the requirements of smart application-based speech recognition systems.

On some differential equations involving a new kind of variable exponents

In this paper, we are concerned with some new first order differential equation defined on the whole real axis R . The principal part of the equation involves an operator with variable exponent p depending on the variable x ∈ R through the unknown solution while the nonlinear part involves the classical variable exponent p ( x ) . Such kind of situation is very related to the presence of the variable exponent and has not been treated before. Our existence result of nontrivial solution cannot be reached using standard variational or topological methods of nonlinear analysis and some sophisticated arguments have to be employed.