Journal of Fundamental Mathematics and Applications (JFMA)
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HOW TO COMBINE VAM AND DIJKSTRA’S ALGORITHM
Get PDFSolving transportation problems sometimes does not only require using one method or algorithm. Sometimes it is necessary to use several methods or algorithms at once. In this research, combining the Vogel’s Approximation Method (VAM) and Dijkstra algorithm can be carried out if three assumptions are met. These three assumptions are based on the characteristics of each VAM and Dijkstra’s algorithm, as well as the compatibility between the two
Regression Analysis for Multistate Models Using Time Discretization with Applications to Patients’ Health Status
Get PDFThis paper addresses the estimation of multistate models in discrete time, which are widely used to describe complex event histories involving transitions between multiple health states. Accurate estimation of transition intensities and probabilities is essential for understanding disease progression and evaluating the impact of covariates. However, conventional estimators such as the Nelson–Aalen estimator often produce rough estimates, especially in sparse data settings. To improve estimation, we apply kernel smoothing to Nelson–Aalen estimators of transition intensities. Transition probabilities are then derived via product-integrals of the smoothed intensities. Covariate effects on transition intensities are modeled using the Cox proportional hazards model. Rather than modeling covariate effects on transition probabilities indirectly through their influence on transition intensities, we model them directly using pseudo-values of state occupation probabilities obtained through a jackknife procedure. These pseudo-values are treated as outcome variables in a Generalized Estimating Equation (GEE) framework. The proposed methodology is applied to patient visit data from a clinic in West Java, Indonesia, where it successfully captures both the progression dynamics across health states and the influence of key covariates
ON PROPERTIES OF PROJECTIVE SPACE DETERMINED BY QUOTIENT MAP
Get PDFThe state of a system in quantum theory is not always described by an element of a Hilbert space but by an element of projective space. The research aims to prove that the real projective space consisting of one-dimensional linear subspaces is a smooth manifold which is constructed by a quotient map. It is shown that a projective space is a Hausdorff space, second countable, and -dimensional locally Euclidean. It is also proved that the -dimensional real a projective space is homeomorphic to the quotient topology . The proof involves a quotient map which is defined by a quotient topology
ON A HIGHLY ROTUND NORM AND UNIFORMLY ROTUND NORM IN EVERY DIRECTION ON A FRECHE’T SPACE
Get PDFThe word rotund comes from Latin word "rotundus" implying wheel-shaped or round (from rota wheel). Rotundity is the roundness of a 3-dimensional object. Some of the properties of rotundity include: UR-Uniformly Rotund, LUR-Locally Uniformly Rotund, MLUR-Midpoint Locally Uniformly Rotund, WUR-Weakly Uniformly Rotund, URED-Uniformly Rotund in Every Direction, HR- Highly Rotund, WLUR-Weakly Locally Uniformly Rotund and URWC-Uniformly Rotund in Weakly Compact sets of directions. Problems on Rotundity properties are still open. Smith gave a summary chart on rotundity of norms in Banach spaces. The chart left an open question whether or not a Highly Rotund norm(HR) implies Uniformly Rotund norm on Every Direction(URED). It is not clear whether if a Banach space has a Highly Rotund(HR) norm it follows that it has and equivalently URED. In this paper, we investigated the relationship between a Highly Rotund norm(HR) and a Uniformly Rotund norm in Every Direction(URED) on a Freche’t Space. The result shows that both Highly Rotund norm and Uniformly Rotund norm on Every Direction(URED) exist in Freche’t spaces. The implication of this result is that rotundity properties can be extended within spaces. This research work is very important since rotundity properties are strongly applicable in many branches of mathematics
TWO-COMPARTMENT PHARMACOKINETIC MODELS WITH SINGLE AND DOUBLE ELIMINATION RATES FOR ORAL ADMINISTRATION OF TWO DRUGS
Get PDFThis paper presents two pharmacokinetic models with two compartments, incorporating both single and double elimination rates for the oral administration of two drugs. The models allow for the estimation of the absorption, distribution, and elimination rate constants. This estimation is performed in two phases based on the time intervals. The first phase estimates the distribution and elimination rates using concentration data from larger time data points, employing residual techniques and least squares error. In contrast, the absorption rate estimation is conducted using the Wagner-Nelson method for smaller time intervals. Prior to these estimations, an analytical solution is required, for which Laplace transformation is utilized. Finally, graphical simulations are performed to observe the dynamics of drug concentrations throughout the processes of absorption, distribution, and elimination. Additionally, these simulations facilitate a comparison between the actual data of drug concentrations in each compartment and their respective approximations
BOILING POINT MODELING OF EUGENOL COMPOUNDS AND ITS DERIVATIVES USING THE SOMBOR INDEX AND REDUCED SOMBOR INDEX APPROACHES
Get PDFEugenol and its derivatives, phenylpropanoid compounds derived from plants like Syzygium aromaticum, exhibit significant biological activities, including antimicrobial, antifungal, anti-inflammatory, antioxidant, analgesic, and anticancer properties. These attributes make them valuable in drug development and medical applications. In mathematical chemistry, chemical topology graphs are used to determine the topological indices of molecules, which to help predict physical and chemical properties. Here, atoms are represented as nodes and bonds as edges. This study explores the relationship between the Sombor index, the reduced Sombor index, and the boiling points of eugenol and its derivatives. The methodology includes literature review and computational analysis of the indices, followed by correlation analysis with the boiling points. The findings reveal that the Sombor index negatively correlates with the boiling point, explains 84.8% of the boiling point variance. This implies that an increase in the Sombor index results in a lower boiling point. Conversely, the reduced Sombor index demonstrates a positive correlation, influencing 36.1% of the boiling point variations, indicating that higher reduced Sombor indices correspond to higher boiling points. When combined, the Sombor and reduced Sombor indices explain 86.4% of the boiling point variance, highlighting their significance as predictive parameters. These results provide insights into the thermal properties of eugenol-based compounds and their potential applications in material and pharmaceutical sciences. By leveraging these indices, researchers can better predict and tailor the physical properties of eugenol derivatives for specific purposes
COORDINATING AND OPTIMIZING TWO-WAREHOUSE INVENTORY SYSTEMS: A MATHEMATICAL PROGRAMMING APPROACH
Get PDFEffective supplier and carrier selection plays a pivotal role in supply chain management, ensuring maximum profitability. This study introduces an innovative decision-support system designed for supplier and carrier selection problems in static two-warehouse inventory systems. The model assumes warehouse collaboration, where warehouses consolidate efforts to fulfill overall demand. To address this, a mathematical programming approach is developed and solved using the LINGO 21.0 optimization software. Experimental results reveal that the proposed model delivers optimal decisions. Even though challenges are still available on the constraint functions and the derivation of parameters' values, the results provide positive managerial insights that offer valuable tools for stakeholders to improve supply chain efficiency
On the necessary and sufficient condition of a k-Euler pair
Get PDFIn this paper, we discuss George Andrews’ definition of an Euler pair andSubbarao’s generalization of the Euler pair to a k-Euler pair. Let N and M be non-empty sets of natural numbers. A pair (N, M) is called a k-Euler pair if, for any natural number n, the number of partitions of n into parts from N is equal to the number of partitions of n into parts from M, with the condition that each part appears fewer than k times. We further explore several theorems concerning Euler pairs that were established by Andrews and Subbarao, and we present proofs using a method distinct from those previously utilized
HPPCv: a Modification of HPPC Scheme with Vinegar Variables
Get PDFThe Hidden Product of Polynomial Composition (HPPC) Digital Signature is multivariate-based cryptography using an HFE trapdoor. The HPPC scheme provides the technique for choosing the HFE central map. Its technique utilizes the product of the composition of two linearized polynomials. In this research, we proposed the modification of the HPPC scheme. We modify the HPPC scheme such that the scheme is based on HFEv. The linearized polynomial with vinegar variables will be chosen for constructing the central map. In our modification version, the public key becomes a system of polynomials of degree 4 and a map from n+v to n-dimension vector space. For a final remark, Despite an increase in the polynomial degree, HPPCv maintains a computational cost similar to HPPC
Construction of the Rough Quotient Modules over the Rough Ring by Using Coset Concepts
Get PDFGiven an ordered pair where is the set universe and is an equivalence relation on the set is called an approximation space. The equivalence relation is a relation that is reflexive, symmetric, and transitive. If the set , then we can determine the upper approximation of the set , denoted by , and the lower approximation of the set , denoted by . The set is said to be a rough set on if and only if . A rough set is a rough module if it satisfies certain axioms. This paper discusses the construction of a rough quotient module over a rough ring using the coset concept to determine its equivalence classes and discusses the properties of a rough quotient module over a rough ring related to a rough torsion module