Divisors of expected Jacobian type

Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of $D$-modules. In this work we are interested on divisors of expected Jacobian type, that is, divisors whose gradient ideal is of linear type and the relation type of its Jacobian ideal coincides with the reduction number with respect to the gradient ideal plus one. We provide conditions in order to be able to describe precisely the equations of the Rees algebra of the Jacobian ideal. We also relate the relation type of the Jacobian ideal to some $D$-module theoretic invariant given by the degree of the Kashiwara operator.

Minimal switching of multiple input multilevel output DC-DC converter

This paper proposes a minimal switching multiple input multilevel output (MS-MIMLO) DC-DC converter. Minimizing the cost of operation is an utmost priority of any electric circuit design. Thus, reduction number of switches that control and manage the operation of feeding power into the MIMLO DC-DC convertors is presented. The proposed MS-MIMLO DC-DC converter exerts many advantages, include high voltage transfer ratio with a small size inductor, reduced power losses and low voltage stress across the semiconductor devices. Beside the highly conversion ratio and efficiency, the characteristics of the proposed converter have a simple configuration with low number of components as well. The MATLAB/Simulink software was implemented to simulate the proposed topology in order to verify the performance of the MS-MIMLO DC-DC converter. The result of simulations demonstrated the benefits of reducing the number of switches without affecting the operation and performance of the MIMLO DC-DC converter circuit.

New Business Segmentation for Haulage Industry in Malaysia

The haulage industry has the biggest fleets as compared to the others road trucking operators in Malaysia. The history of haulage industry started in 1971 until 2004 with five operators and in 2019 and above was recorded to 220 operators in the market. It was demonstrated with the open market which the growth of total fleet from 2,131 prime movers and 10,701 trailers before 2004 and more than 4,500 over prime movers and 31,500 over trailers in 2018 (AMH, 2018). The total number of prime movers and trailers had increased to 111% to overall fleets’ capacity. Haulage market which relate to container throughputs form 2009 - 2019 (ten-year) recorded at 16 million tues to 25 million teus in 2019 (UNCTAD 2019) which increased only by 65%. It was calculated on the surplus by 46 % of holding of prime movers in haulage industry at present. Apparently the market of haulage industry has stagnant and invite further sluggishness on haulage movements. The haulage operators had initiated to downsizing on the fleets due to unstable market and difficulty to sustain in their business. Therefore, the research suggests on appropriate ways to improve on the present condition and making more competitiveness of haulage industry. This research will investigate into three (3) segmentations such as reduction number of fleets, improvement on present activities and changing on other types of trucking businesses. The key respondents of the survey were the haulage operators, customers, government agency and other stakeholders. The survey was conducted among 200 respondents and at the end only 170 answers were accepted. The research uses SPSS version 25 and PLS-SEM to analyze from the collected data. The finding of the research has suggested that the three segmentations are the most appropriate ways to improve the present condition in haulage industry.

Pullback of the Normal Module of Ideals with Low Codimension

The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen–Macaulay.

Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

In this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus

A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable. Keywords: Malaria; Dengue Fever; Co-infection; Basic reproduction number; Disease-Free equilibrium

On the reduction numbers of monomial ideals

Let [Formula: see text] be a monomial ideal in a polynomial ring with two indeterminates over a field. Assume [Formula: see text] is contained in the integral closure of some ideal that is generated by two elements from the generating set of [Formula: see text]. We produce sharp upper bounds for each of the reduction number and the Ratliff–Rush reduction number of the ideal [Formula: see text]. Under certain hypotheses, we give the exact values of these reduction numbers, and we provide an explicit method for obtaining these sharp upper bounds.