The English Galileo: Thomas Harriot and the Force of Shared Knowledge in Early Modern Mechanics

I discuss the work of the English mathematician and philosopher Thomas Harriot (1560–1621), analyzing especially his work on projectile motion, and comparing it to that of his contemporary Galileo Galilei (1564–1642). I argue that although their work on projectile motion was carried out independently and displays both similarities and differences, it shows that they focused on common challenging objects of study that embodied what I term “points of contact” between preclassical and classical mechanics. I also argue that their shared knowledge defined the space of possible solutions to the problem of projectile motion, although the inferential pathways they followed through their shared knowledge proceeded in exactly opposite directions. I conclude that their work suggests that the lines of development in early modern mechanics converged in such a way that the long-term development of science was largely unaffected by the peculiarities in an individual scientist’s work.     

Scheduling uniform parallel machines subject to a secondary resource to minimize the number of tardy jobs

This research investigates the problem of scheduling jobs on a set of parallel machines where the speed of the machines depends on the allocation of a secondary resource. The secondary resource is fixed in quantity and is to be allocated to the machines at the start of the schedule. The scheduling objective is to minimize the number of tardy jobs. Two versions of the problem are analyzed. The first version assumes that the jobs are pre-assigned to the machines, while the second one takes into consideration the task of assigning jobs to the machines. The paper proposes an Integer Programming formulation to solve the first case and a set of heuristics for the second.     

Online scheduling of parallel jobs on two machines is 2-competitive

We consider online scheduling of parallel jobs on parallel machines. For the problem with two machines and the objective of minimizing the makespan, we show that 2 is a tight lower bound on the competitive ratio. For the problem with m machines, we derive lower bounds using an ILP formulation.     

The changing scenario of the atomic nucleus—from nucleons and mesons to quarks and gluons

The general characteristics of the transition from hadronic matter of nucleons, three quark bags, mesons of quark antiquark pairs to quark gluon plasma is discussed. The phenomenological approach essentially guided by the MIT bag model and general thermodynamic criteria of first-order phase transition is elaborated. The more realistic calculations using the QCD lattice renormalization quark are touched upon. Possible signals of quark-gluon plasma are discussed. The central issue of deciphering plasma signals from the signals of hot hadronic matter is discussed in detail. The signals of the quark-gluon plasma, a subject of considerable interest in contemporary literature are focussed only on (i) dileptons (ii) photon photon pairs and (iii)J/Ψ suppression (with special emphasis on CERN experiments). The lingering shadow of “EMC” effect is also mentioned. Relics of the very early universe microseconds after the big bang in today’s universe (∼ 15 billion years later) are discussed. Finally, the outlook of this very exciting field is presented, a purely personal viewpoint, generalized eventually to poetic signals of the creation of the universe.     

Is a Spatially Closed Universe Possible?

The present speculation shows that a spatially closed geometry might be an alternative to Inflation scenario.     

Mathematical Optimization of in vivo NMR Chemistry Through the Fast Padé Transform: Potential Relevance for Early Breast Cancer Detection by Magnetic Resonance Spectroscopy

Mathematical advances in signal processing through the fast Padé transform (FPT) can greatly improve the information extracted via in vivo nuclear magnetic resonance (NMR) chemistry. The FPT is a frequency-dependent, non-linear rational polynomial approximation of the exact Maclaurin series, which dramatically improves resolution and signal-to-noise ratio in a stable manner with robust error analysis and provides precise numerical data for all the peak parameters (position, height, width and phase) for every true resonance including those that are weak and/or overlapping. The concentrations of many of the chemical constituents of tissues can thereby be accurately determined. These advantages of the FPT are particularly germane for in vivo NMR detection and quantification of a number of molecular markers of breast cancer, such as phosphocholine, as well as lactate, which cannot be assessed using standard Fourier data analytical techniques applied to in vivo NMR in the clinical setting.     

Neural Wave Representation in Early Vision

The neural wave representation which describes spatiotemporal information in early vision is proposed in terms of extended Gabor functions in this paper. Its reasonability, completeness and uncertainty in spatiotemporal domains and their frequency domains were investigated. The ranges of these parameters in this representation were estimated on electrophysiological and psychophysical data. We derived the partial differential equations which the neural wave satisfied. The general significance of 3D neural wave representation has been explored.     

ANALYSIS AND EXPERIMENT ON TRANSIENT DYNAMIC RESPONSE IN FINITE MINDLIN PLATE

The transient wave propagation in the finite rectangular Mindlin plate is investigated by the analytical and experimental methods. The generalized ray method (GRM) which has been successfully applied to study the transient responses of beams, planar trusses, space frames and infinite layered media is extended to investigate the transient wave propagation and early short time transient response in finite Mindlin plate. Combining the wave solution, the shock source and the boundary conditions, the ray groups transmitted in the finite rectangular plate can be determined. Numerical simulations and experiments are performed and compared with each other. The results show that the transient wave propagation and early short time transient responses in the finite plate can be studied using the GRM. The early short time transient accelerations are very large for the finite plate subjected to the unit impulse, while the early short time transient displacements are very small. The early short time transient accelerations under the unit impulse are much larger than those under the unit step impulse. The thickness and material characteristics have remarkable effects on the early short time transient responses.     

A discrete-time retrial queueing model with one server

This paper presents a one-server queueing model with retrials in discrete-time. The number of primary jobs arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each job requires from the server a generally distributed number of slots for its service, and the service times of the different jobs are independent. Jobs arriving in a slot can start their service only at the beginning of the next slot. When upon arrival jobs find the server busy all incoming jobs are sent into orbit. When upon arrival in a slot jobs find the server idle, then one of the incoming jobs (randomly chosen) in that slot starts its service at the beginning of the next slot, whereas the other incoming jobs in that slot, if any, are sent into orbit. During each slot jobs in the orbit try to re-enter the system individually, independent of each other, with a given retrial probability.     

早期护理干预在新生儿黄疸治疗效果的影响

目的探讨早期护理干预对新生儿黄疸治疗效果的影响。方法对照组患儿采取常规护理,实验组患儿采取早期护理干预。观察患儿胎便初排时间和胎便转黄时间;观察患儿干预前后血清胆红素、体质量变化情况。结果实验组患儿胎便初排时间和胎便转黄时间均低于对照组,差异有统计学意义(P0.05),实验组患儿干预后血清胆红素、体质量均优于干预前和对照组,差异有统计学意义(P0.05),对照组患儿干预后血清胆红素优于干预前,差异有统计学意义(P0.05)。结论早期护理干预对新生儿黄疸治疗效果有积极的影响,能够缩短患儿胎便初排时间和胎便转黄时间,改善患儿血清胆红素、体质量水平。