On the Reduction of Singularly-Perturbed Linear Differential Systems

In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is based on the reduction criterion introduced for linear singular differential systems by Moser. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations, giving rise to the package ISOLDE, as well as in the perturbed algebraic eigenvalue problem. Our algorithm, implemented in the computer algebra system Maple, paves the way for efficient symbolic resolution of singularly-perturbed linear differential systems as well as further applications of Moser-based reduction over bivariate (differential) fields.Comment: Keywords: Moser-based Reduction, Perturbed linear Differential systems, turning points, Computer algebr

Formal Solutions of a Class of Pfaffian Systems in Two Variables

In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in (Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE, implemented in the computer algebra system Maple.Comment: Keywords: Linear systems of partial differential equations, Pfaffian systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal for

Development of new transition metal catalyzed C-C bond forming reactions and their application toward natural product synthesis

textIn Michael J. Krische research group we are developing new transition metal catalyzed Carbon-Carbon (C-C) forming reactions focusing on atom economy and byproduct free, environmental friendly approaches. We have developed a broad family of C-C bond forming hydrogenations with relative and absolute stereocontrol which provide an alternative to stoichiometric organometallic reagents in certain carbonyl and imine additions. Inspiring from the group work my goal was to develop new reactions, extend the scope of our group chemistry and their application towards synthesis of biologically active natural products. I have been part of enantioselective Rh catalyzed Aldol reaction of vinyl ketones to different aldehydes. Also, we have found that iridium catalyzed transfer hydrogenation of allylic acetates in the presence of aldehydes or alcohols results in highly enantioselective carbonyl allylation under the conditions of transfer hydrogenative. Based on this reactivity a concise enantio- and diastereoselective synthesis of 1,3-polyols was achieved via iterative chain elongation and bidirectional iterative asymmetric allylation was performed, which enables the rapid assembly of 1,3-polyol substructures with exceptional levels of stereocontrol. The utility of this approach stems from the ability to avoid the use of chirally modified allylmetal reagents, which require multistep preparation, and the ability to perform chain elongation directly from the alcohol oxidation level. This approach was utilized for the total synthesis of (+)-Roxaticin from 1,3-propanediol in 20 longest linear steps and a total number of 29 manipulations. Further, advancements were made in iridium catalyzed C-C bond formation under transfer hydrogenation. While methallyl acetate does not serve as an efficient allyl donor, the use of more reactive leaving group in methallyl chloride compensate for the shorter lifetime of the more highly substituted olefin π-complex. Based on this insight into the requirements of the catalytic process, highly enantioselective Grignard-Nozaki-Hiyama methallylation is achieved from the alcohol or aldehyde oxidation levels. Also, a catalytic method for enantioselective vinylogous Reformatsky- type aldol addition was developed in which asymmetric carbonyl addition occurs with equal facility from the alcohol or aldehyde oxidation level. Good to excellent levels of regioselectivity and uniformly high levels of enantioselectivity were observed across a range of alcohols and aldehydes.Chemistr

Selective hydrogenation of citral over mesoporous Ru/TiO2/SiO2 catalysts

Thesis (Master)--Izmir Institute of Technology, Chemical Engineering, Izmir, 2013Includes bibliographical references (leaves: 68-72)Text in English; Abstract: Turkish and Englishxiii, 84 leavesThe liquid phase citral hydrogenation was investigated over Ru/SiO2, Ru/TiO2 and Ru/TiO2/SiO2 catalysts. TiO2/SiO2 supports were prepared by sol-gel deposition, impregnation and absorption methods. The effect of the supports and catalyst reduction temperature, 300 ï‚°C (LTR) and 450 ï‚°C (HTR) on citral conversion and selectivity to unsaturated alcohols were examined. A well-defined crystalline anatase phase was only observed on the support prepared by absorption method, TiO2/SiO2-ABS. A high dispersion and interaction of Ru were observed over TiO2 for Ru/TiO2. Ru/TiO2/SiO2-ABS also displayed similar properties but to a lower extent. Ru/TiO2/SiO2-ABS catalyst showed the highest citral conversion (57.7 %) at LTR among the different Ru/TiO2/SiO2 catalysts. Its selectivity to UA was also high (70.2 %). This was attributed to a better metal support interaction and dispersion obtained by this method. However, a selectivity of 62.6 % was obtained over Ru/TiO2. Activity of the catalysts was mostly observed to decrease as reduction temperature increased from 300 ï‚°C to 450 ï‚°C. Citral conversion decreased from 57.7 % to 42.3 % over Ru/TiO2/SiO2-ABS. However, selectivities to unsaturated alcohol (nerol and geraniol) over Ru/TiO2 and Ru/TiO2/SiO2 catalysts were increased at HTR, reaching about 80 %. This was suggested to be due to more interaction of TiO2 with the Ru (strong metal support interaction). There was no significant change in the selectivity to UA obtained at HTR for Ru/SiO2. This was related to the inert nature of SiO2

What is Multiphysics? Definition and Examples

Academic presentation at the International Conference on the Cooperation and Integration of Industry, Education, Research and Application, arranged by Henan University of Science and Technology, Luoyang, 21. - 23.11.23

Evaluation of the Surgical and Pharmacological Treatment of Diabetic Foot Infection: A Retrospective Study

BACKGROUND: Diabetic foot infection is a major cause of patient disabilities and lowers limb amputations, with high treatment costs and hospitalisation requirements. AIM: Aim of this study was to evaluate surgical wound care plus antibiotic effects in the treatment of mild and moderate diabetic foot infections. METHODS: This retrospective study involved 60 patients with diabetic foot infections with or without osteomyelitis. The patients were categorised as group 1 mild and group 2 moderate. Both groups were treated using local wound debridement and the systemic administration of antibiotics. Group 1 (16) patients were treated with two regimens of oral antibiotics in two regimens, A (amoxicillin/clavulanate + metronidazole) and B (clindamycin + metronidazole), for 10-14 days. Group 2 (42) patients were treated with oral plus intravenous antibiotics in two regimens, A (ampicillin + cloxacillin + metronidazole) and B (lincomycin + metronidazole), for 6 weeks. The patients followed-up with local wound care specialists for 3 months to evaluate the treatment outcomes (cure, improvement, or failure). RESULTS: Group 1 had an 80% cure rate under regimen A and a 100% cure rate under regimen B. Group 2 regimen A patients had a 61.5% cure rate and 11.53% improved, while regimen B patients had a 68.75% cure rate and 12.5% improved. Failure in both regimens was 23.8% in 20 patients with osteomyelitis, while 35% were cured and 20% improved during the study period. CONCLUSION: Local surgical wound care for 3 months with antibiotic regimens for 6 weeks resulted in good response and cure rates, with lower costs and fewer instances of hospitalisation. Intravenous lincomycin and oral metronidazole achieved higher cure responses for moderate diabetic foot infections

A study on relationship among free cash flow, firm value and investors’ cautiousness: Evidence from Tehran Stock Exchange

Financial statements as well as financial standards are always considered as primary sources for getting rich information of firms. The standards are normally divided in two categories of economic and accounting and each of these standards shows one of the specifications of the company and has its own advantageous and disadvantageous. There are different standards, which are used for firm assessment. Therefore, a company with more gained prominences has more change to succeed in attracting credits and financing from the capital market. Under such circumstances, such a company can attract more finance and it can be sold sooner on the stock exchange. This paper tries to investigate on the free cash flow as an effective factor in specifying the real value of the business enterprises on 56 selected firms from Tehran Stock Exchange. The results of this study have disclosed that, there was a direct and meaningful relationship between free cash flow of the business enterprises and their real values. Second, the real values of the business enterprises are more than their predicted values. Finally, the predicted value of the business enterprises on the basis of the free cash flow is more than their market value

Cyclic Behavior of Steel Beam-to-Column Moment Connections Using Different Sizes of Flange Plates and Reinforced by a Single Rib Plate

This paper presents a numerical study on the behavior of connection between steel I-beam and H-column when are affected by cyclic loading. The connection used the flange plates to connect the beam flanges to the column flange. They were welded to the top and bottom flange plates and created a welded flange plate (WFP) connection. Specimens were six models of WFP connections with different beam geometry and flange plate sizes which were modeled and their cyclic behavior were investigated using finite element analysis in ABAQUS program. Three of them were reinforced by a vertical triangular top and bottom rib plates, and others remained unreinforced. The results showed that reinforcement with a vertical triangular rib plate attached to the top and bottom flange plates can improve cyclic behavior of WFP connections.  By using a rib plate, the equivalent plastic strain was increased and showed better plastic hinge formation compared to those with no vertical rib plate. Those models with IPB beam sections had the best cyclic behavior compared to those with IPE beam sections and satisfied the acceptance criteria of AISC seismic provisions for intermediate and special moment frames. We concluded that those WFP connections which did not satisfy the criteria of AISC seismic provisions for special moment frames, can be upgraded by a vertical triangular rib plate in order to be used in special moment frames