scholarly journals Lattice function measurements in the Fermilab Accumulator Ring

2002 ◽  
Author(s):  
M. Church
Keyword(s):  
Lattice Function

Automatic differentiation and lattice function matching

1997 ◽  
Author(s):  
Jean-François Ostiguy ◽  
Leo Michelotti ◽  
James A. Holt
Keyword(s):  
Automatic Differentiation ◽  
Lattice Function

scholarly journals System of Laser Monitoring of Water Pollution with Application of Relative Description of Signal Shape

2020 ◽  
Vol 11 (2) ◽  
pp. 114-121
Author(s):  
V. A. Alekseev ◽  
S. I. Yuran ◽  
V. P. Usoltsev ◽  
D. N. Shulmin
Keyword(s):  
Water Pollution ◽  
Spectral Characteristics ◽  
Measurement Data ◽  
Rational Approach ◽  
Relationship Matrix ◽  
Design Basis ◽  
Separate Branch ◽  
Lattice Function ◽  
Design Basis Accident ◽  
Laser Monitoring

As a rule, the wastewater treatment system is not designed to filter substances formed, as a result of beyond design basis accident. The nature of the beyond design basis accident is associated with the shortterm appearance of a clot of these substances in wastewater, determined by the volume of the substance storage tank. Therefore, a rational approach is to divert this portion of the formed substances into a separate branch of the sewage system or sedimentation tanks. The aim of the work is to implement this approach by creating a laser monitoring system for water pollution.The article proposes a system for automatic detection of a clot of emergency discharge of pollutants into the wastewater of an industrial enterprise. The structural diagram of the system and the purpose of its main elements are given. The system should provide clot detection in real time. To ensure this function, a preliminary study is made of the spectral characteristics of all substances that may appear in wastewater in the event of an emergency.Based on these data, the wavelengths of laser radiation in the system are selected. The obtained measurement data from several probes are presented in the form of a lattice function, which is translated into a relative description representing the order relationship matrix on the set of lattice function components. The relative description is invariant to linear changes in the lattice function. The decision to detect any substance from emergency discharges is made based on a comparison of the relative description of the measurements with the standards prepared at the stage of system setup.The article provides an example of the formation of standards for emergency clots from glycerin and allyl alcohol. The graphs of the lattice functions obtained from the IR spectra of emergency discharges of these substances are given; algorithms for constructing a lattice function and comparison of lattice functions. Thus, using the developed mathematical description of the shape of digital signals based on the relative description, the signal of the monitoring curve can be described in the form of a curve of the optical density change of an aqueous medium.

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

Plant-Herbivore Coevolution in a Spatially and Genetically Explicit Model

1995 ◽  
Vol 2 (2) ◽  
pp. 239-259 ◽  
Author(s):  
Gregg Hartvigsen ◽  
William T. Starmer
Keyword(s):  
Plant Defense ◽  
Relative Increase ◽  
Dispersal Distance ◽  
Encounter Rate ◽  
Gene Frequencies ◽  
Herbivore Resistance ◽  
Encounter Rates ◽  
Spatial Lattice ◽  
Lattice Function ◽  
And Function

A coevolutionary model was developed to test interactions between diploid plants and herbivores using genetic algorithms on a spatial lattice. Simulated plants carried defensive genes and herbivores carried genes coding for resistance (metabolism of herbivore defense) in gene-for-gene synchrony. Collectively these genes are referred to as defensive/resistance genes (DR-genes). Genes were linked on chromosomes. Regulatory genes modified both dominance at these DR loci and the tradeoff cost involved in producing either defense or resistance. We tested the effects of varying a) the number of DR-loci, b) the ratio of the number of herbivore:plant generations, c) the shape (square vs. long and thin) and function (torus vs. island) of the lattice, and d) herbivore encounter rate on plant progeny dispersal distance. Increasing both the number of DR-genes and the ratio of herbivore:plant generations caused a tighter coevolutionary response between plants and herbivores. Plant defense was highly sensitive to herbivory but not to increasing encounter rates. Plant DR-genes were selectively disadvantageous with only one lucus but selectively favored with two or more loci. Increasing the number of herbivore:plant generations caused increased fluctuations in herbivore resistance gene frequencies and a decrease in the lag time in herbivore response to changes in plant defensive gene frequencies. The relationship between heterotroph and autotroph DR-genes increased exponentially with increasing numbers of DR-loci. This relationship suggests that autotrophs benefit from increased diversity of defense that causes a relative increase in cost for the heterotrophs. The shape of the lattice interacted with lattice function, resulting in high species persistence on wraparound habitats and the greatest extinction likelihood on rectangular islands. Low to moderate herbivore encounter rates increased plant progeny dispersal distance while high herbivore encounter rates tended to reduce dispersal distance. The frequencies of genes coding for plant defense and herbivore resistance were dynamic for thousands of generations, despite the homogeneous lattice. This interaction may increase extinction probabilities in fragmented habitats.

A fast algorithm for maximizing a non-monotone DR-submodular integer lattice function

2020 ◽  
Vol 840 ◽  
pp. 177-186
Author(s):  
Qingqin Nong ◽  
Jiazhu Fang ◽  
Suning Gong ◽  
Yan Feng ◽  
Xiaoying Qu
Keyword(s):  
Fast Algorithm ◽  
Integer Lattice ◽  
Lattice Function

scholarly journals IX. Memoir on the theory of the partitions of numbers. - Part VI. Partitions in two-dimensional space, to which is added an adumbration of the theory of the partitions in three-dimensional space

1912 ◽  
Vol 211 (471-483) ◽  
pp. 345-373 ◽  
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Dimensional Space ◽  
A Priori ◽  
Three Dimensional ◽  
Large Measure ◽  
Lattice Function ◽  
The Subject ◽  
Definition Of

I Resume the subject of Part V. of this Memoir by inquiring further into the generating function of the partitions of a number when the parts are placed at the nodes of an incomplete lattice, viz., of a lattice which is regular but made up of unequal rows. Such a lattice is the graph of the line partition of a number. In Part V. I arrived at the expression of the generating function in respect of a two- row lattice when the past magnitude is unrestricted. This was given in Art. 16 in the form GF ( ∞ ; a, b ) = (1) + x b +1 (a - b) / (1) (2) ... (a+1). (1) (2) ... (b). I remind the reader that the determination of the generating function, when the part magnitude is unrestricted, depends upon the determination of the associated lattice function (see Art. 5, loc . cit .). This function is assumed to be the product of an expression of known form and of another function which I termed the inner lattice function (see Art. 10, loc . cit .), and it is on the form of this function that the interest of the investigation in large measure depends. All that is known about it à priori is its numerical value when x is put equal to unity (Art. 10, loc cit . The lattice function was also exhibited as a sum of sub-lattice functions, and it was shown that the generating function, when the part magnitude is restricted, may be expressed as a linear function of them. These sub-lattice functions are intrinsically interesting, hut it will be shown in what follows that they are not of vital importance to the investigation. In fact, the difficulty of constructing them has been turned by the formation and solution of certain functional equations which lead in the first place to the required generating functions, and in the second place to an exhibition of the forms of the sub-lattice functions. To previous definitions I here add the definition of the inner lattice function when there is a restriction upon the part magnitude, and it will be shown that the generating, lattice, and inner lattice functions satisfy certain functional equations both when there is not and when there is a restriction upon the part magnitude.

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