Logarithmic Addition Research Articles

Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies

The paper defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the basic entropy is a ϕ-deformed one, in the sense of Naudts, is investigated in detail, with emphasis on the variation of the emergent scalar curvatures. Moreover, the paper highlights the impact on these geometries determined by the addition of some group logarithms.

Relationships between Size Distribution, Morphological Characteristics, and Viscosity of Cellulose Nanofibril Dispersions.

Rheological parameters of cellulose nanofibril dispersions (CNF) are relevant and commonly used as quality control for producing of this type of material. These parameters are affected by morphological features and size distribution of the nanofibrils. Understanding the effect of size distribution is essential for analyzing the rheological properties, viscosity control, performance of CNFs, and potential dispersion applications. This study aims at comprehending how the morphological characteristics of the CNFs and their size distribution affect the rheological behavior of dispersions. The CNF dispersions were fractionated by size, obtaining six fractions of each, which were analyzed for their morphology and rheology (viscosity, intrinsic viscosity). In the dilute region, the viscosity and intrinsic viscosity behavior of CNF dispersions are linear concerning the size distribution present in the dispersion. In the semi-dilute region, the size of the fibrils and the fiber aggregates have a relevant effect on the viscosity behavior of CNF dispersions, which are satisfactorily related (R2 = 0.997) using the rule of logarithmic additivity of the dispersion viscosities of size fractions.

ULog: a software-based approximate logarithmic number system for computations on SIMD processors

This paper presents a new number representation based on logarithmic number system (LNS) called unsigned logarithmic number system (ulog), as an alternative to the conventional floating-point (FP) number format, to use in approximate computing applications. ulog is tailored for software implementation on commercial general-purpose processors, and uses the same dynamic range as conventional IEEE Standard FP formats to prevent overflow and underflow. ulog converts FP numbers to fixed-point numbers and uses integer operations for all computations. Moreover, vectorization and approximate logarithmic addition have been used to increase the performance of the software implementation of ulog. Then, we used different BLAS benchmarks to evaluate the performance of the proposed format than IEEE standard formats. 16- and 32-bit ulog improve the runtime than double-precision at most 70.26% and 46.36%, respectively. Besides, accuracy analysis of the ulog based on different logarithm bases showed that base 4 has the lowest error in most cases.

On the Possibility of a Radical Increase in Thermal Conductivity by Dispersed Particles

Theoretical and experimental data on the effect of additions of micro- and nanosized solid particles on the thermal conductivity of liquid media (nanofluids) are considered. According to theoretical calculations, a manifold increase in the thermal conductivity is possible only for resting media in which percolation structures are formed from the modifier nanoparticles, whereas in the case of the coolant circulation and/or random distribution of particles in its volume the increase in the thermal conductivity cannot increase several tens of percents. The primary factors for increasing the thermal conductivity are high volume fraction of particles and isotropicity of their properties, whereas the specific thermal conductivity of the particle material is not a key factor. The available experimental data were obtained using different measurement methods and different dispersions whose structure was not duly controlled. Therefore, the data are characterized by large scatter, which does not allow unambiguous identification of the acting averaging law, although the majority of data are characterized by positive deviation from Maxwell’s law. On the other hand, the available data do not exceed the values expected on the basis of the rule of logarithmic additivity of the component thermal conductivities.

RISC Conversions for LNS Arithmetic in Embedded Systems

The paper presents an original methodology for the implementation of the Logarithmic Number System (LNS) arithmetic, which uses Reduced Instruction Set Computing (RISC). The core of the proposed method is a newly developed algorithm for conversion between LNS and the floating point (FLP) representations named “looping in sectors”, which brings about reduced memory consumption without a loss of accuracy. The resulting effective RISC conversions use only elementary computer operations without the need to employ multiplication, division, or other functions. Verification of the new concept and related developed algorithms for conversion between the LNS and the FLP representations was realized on Field Programmable Gate Arrays (FPGA), and the conversion accuracy was evaluated via simulation. Using the proposed method, a maximum relative conversion error of less than ±0.001% was achieved with a 22-ns delay and a total of 50 slices of FPGA consumed including memory cells. Promising applications of the proposed method are in embedded systems that are expanding into increasingly demanding applications, such as camera systems, lidars and 2D/3D image processing, neural networks, car control units, autonomous control systems that require more computing power, etc. In embedded systems for real-time control, the developed conversion algorithm can appear in two forms: as RISC conversions or as a simple RISC-based logarithmic addition.

CONSIDERATION OF THE VALIDITY OF THE STATISTICAL CHARACTERISTICS OF pH IN SURFACE WATERS

Abstract: pH is one of the most important parameters characterizing the state of water systems. The arithmetic mean values of samples are often used when averaging serial pH measurements in water bodies, as is usually done for other characteristics of the state of the natural environment (temperature, salinity, oxygen concentrations, suspended solids, etc.). However, in this case such an operation is illegal, since the addition of logarithms, which by definition are pH, is non-additive. The authors conducted a study to determine the extent to which pH variability in natural objects such an operation would not distort the results. For this, several samples of the pH index were generated in various ranges of its theoretically possible and natural variability. It was established that with pH variability of less than a unit characteristic of marine pH values, the statistical characteristics of the indicator and [H+ ] concentrations differ slightly, and the medians of the samples coincide. It is concluded that with such ranges characteristic of the waters of the oceans, there is no need to recalculate previously obtained results. However, for the estuaries of rivers flowing into tidal seas, as shown by field measurements, the pH variability in the mixing zone of sea and river waters is several times higher. Similar situations may occur when heavy precipitation falls on the water surface, as well as during floods. In these cases, a simple averaging of the pH values will no longer be correct. In such cases, the use of other averaging algorithms and the choice of stable statistical characteristics are required.

Modeling of elastic-strength properties of elastomers

Model "structure-property", which takes into account the structural heterogeneity of polymer compositions has been developed. Experimental compositions based on styrene-butadiene rubber SCS 30ARK and crosslinked, high viscosity polymer (high-molecular filler - VMN) in different proportions, as well as softeners (industrial oil I-12A, oil PN-6, low-molecular polybutadiene PBN) were investigated. Samples that differ significantly in viscosity were obtained. The rubber blends and vulcanizates, based on the experimental of polymer compositions, were prepared. Physico-mechanical properties - tensile strength, elongation at break, Shore A. A hardness were determined. For describe the physical and mechanical properties of polymers logarithmic additivity rule was used. The properties of the polymer composition (PС) were determined by a single dominant component (resin composition consisting of a high rubber and a filler) and further components (softeners). Identification algorithm consists of four steps. The implementation of this algorithm is carried out using experimental design techniques. Estimation of the unknown parameters in the equation was carried out using the method of least squares. Quality evaluation of the model was conducted with the criteria Fisher, turning points, the Durbin-Watson, R / S-criterion. It is found that the model adequately describes the change of physicomechanical properties depending on the composition of polymer compositions. 3d graphics of the physical-mechanical properties of the polymer compositions were built. This allowed us to estimate the contribution of the dominant component and optional components (including combinations thereof) to change the parameters. It has been established that the introduction of rubber in total more than 50% of the components (BMH and softeners) reduced conventional tensile strength and dramatically increases the relative error of model calculations. (BMH and softeners) reduced conventional tensile strength and dramatically increases the relative error of model calculations.

The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function

For an arbitrary subharmonic function not identically equal to −∞ in a domain D of the complex plane C, we prove the existence of a nonzero holomorphic function in D the logarithm of whose modulus is majorized by locally averaging a subharmonic function with logarithmic additions or even without them in the case D = C.

Hyperbolic statics in space-time

Based on the concept of a material event as an elementary material source that is concentrated on a metric sphere of zero radius—a light cone of Minkowski space-time, we deduce an analog of Coulomb’s law for a hyperbolic space-time field universally acting between space-time events. The collective field that provides interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb part and a logarithmic addition. We find that the Coulomb part depends on a fine balance between the causal and geometric space-time characteristics (a concordance of two regularizations).

Fluorescence Quenching Determination of Uranium (VI) Binding Properties by Two Functional Proteins: Acetylcholinesterase (AChE) and Vitellogenin (Vtg).

The interactions between uranium and two functional proteins (AChE and Vtg) were investigated using fluorescence quenching measurements. The combined use of a microplate spectrofluorometer and logarithmic additions of uranium into protein solutions allowed us to define the fluorescence quenching over a wide range of [U]/[Pi] ratios (from 1 to 3235) at physiologically relevant conditions of pH. Results showed that fluorescence from the two functional proteins was quenched by UO2 (2+). Stoichiometry reactions, fluorescence quenching mechanisms and complexing properties of proteins, i.e. binding constants and binding sites densities, were determined using classic fluorescence quenching methods and curve-fitting software (PROSECE). It was demonstrated that in our test conditions, the protein complexation by uranium could be simulated by two specific sites (L1 and L2). The obtained complexation constant values are log K1 = 5.7 (±1.0), log K2 = 4.9 (±1.1); L1 = 83 (±2), L2 = 2220 (±150) for U(VI) - Vtg and log K1 = 8.1 (±0.9), log K2 = 6.6 (±0.5), L1 = 115 (±16), L2 = 530 (±23) for U(VI)-AChE (Li is expressed in mol/mol of protein).

Representation of the Viscosity of Molten Alloy as a Function of the Composition and Temperature

Although the viscosity of molten metal is very important, the measurement is considerably difficult for high temperature melts. The author's group has developed an oscillating viscometer for high temperature metal. The prediction of the viscosity behavior of the alloys is most useful task because the experimental data acquisition is not easy. In the prediction process, important issue is the composition and temperature dependence. The author has found that the additivity of the logarithmic viscosity was dominant criteria on the composition dependence based on the result of Fe–Si binary melt. Therefore, the logarithmic additivity was adapted to some nickel based super-alloys which were multi component systems. The viscosities of nickel based five binary melts were measured for the representation of the viscosities of super-alloys. The formulation was done by using the separation of variables method. The pre-exponential term and the activation energy were separately approximated as a function of the composition. The results of the approximation successfully represented the viscosities of molten super-alloys.

GSFAP adaptive filtering using log arithmetic for resource-constrained embedded systems

Adaptive filters are widely used in many applications of digital signal processing. Digital communications and digital video broadcasting are just two examples. Traditionally, small embedded systems have employed the least computationally intensive filter adaptive algorithms, such as normalized least mean squares (NLMS). This article shows that FPGA devices are a highly suitable platform for more computationally intensive adaptive algorithms. We present an optimized core which implements GSFAP. GSFAP is an algorithm with far superior adaptation properties than NLMS, and with only slightly higher computational complexity. To further optimize resource requirements we use logarithmic arithmetic, rather than conventional floating point, within the custom core. Our design makes effective use of the pipelined logarithmic addition units, and takes advantage of the very low cost of logarithmic multiplication and division. The resulting GSFAP core can be clocked at more than 80MHz on a one million-gate Xilinx XC2V1000-4 device. The core can be used to implement adaptive filters of orders 20 to 1000 performing echo cancellation on speech signals at a sampling rate exceeding 50kHz. For comparison, we implemented a similar NLMS core and found that although it is slightly smaller than the GSFAP core and allows a higher signal sampling rate for the corresponding filter orders, the GSFAP core has adaptation properties that are much superior to NLMS, and that our core can provide very sophisticated adaptive filtering capabilities for resource-constrained embedded systems.

Determinations of Uranium(VI) Binding Properties with some Metalloproteins (Transferrin, Albumin, Metallothionein and Ferritin) by Fluorescence Quenching

The interactions between uranium and four metalloproteins (Apo-HTf, HSA, MT and Apo-EqSF) were investigated using fluorescence quenching measurements. The combined use of a microplate spectrofluorometer and logarithmic additions of uranium into protein solutions allowed us to define the fluorescence quenching over a wide range of [U]/[Pi] ratios (from 0.05 to 1150) at physiologically relevant conditions of pH. Results showed that fluorescence from the four metalloproteins was quenched by UO(2)(2+). Stoichiometry reactions, fluorescence quenching mechanisms and complexing properties of metalloproteins, i.e. binding constants and binding sites densities, were determined using classic fluorescence quenching methods and curve-fitting software (PROSECE). It was demonstrated that in our test conditions, the metalloprotein complexation by uranium could be simulated by two specific sites (L(1) and L(2)). Results showed that the U(VI)-Apo-HTf complexation constant values (log K(1)=7.7, log K(2)=4.6) were slightly higher than those observed for U(VI)-HSA complex (log K(1)=6.1, log K(2)=4.8), U(VI)-MT complex (log K(1)=6.5, log K(2)=5.6) and U(VI)-Apo-EqsF complex (log K(1)=5.3, log K(2)=3.9). PROSECE fitting studies also showed that the complexing capacities of each protein were different: 550 moles of U(VI) are complexed by Apo-EqSF while only 28, 10 and 5 moles of U(VI) are complexed by Apo-HTf, HSA and MT, respectively.

Influence of coal thermoplastic properties on coking pressure generation: Part 2 – A study of binary coal blends and specific additives

A number of coal blends and pitch/coal blends were evaluated using rheometry, thermogravimetric analysis and microscopy to confirm and further elucidate the coking pressure mechanism previously proposed by Duffy et al. (2007) [1]. We confirm that blending a low rank, high fluidity, low coking pressure coal, with a high rank, low fluidity, high coking pressure coal can significantly reduce the coking pressure associated with the latter. Interestingly, blending does not necessarily result in a fluidity that is midway between that of the two coals; sometimes the fluidity of the blend is less than that of the low fluidity coal, especially when the coals are significantly different in rank. This occurs because the increase in complex viscosity ( η*) through resolidification of the low rank, high fluidity coal counteracts the reduction in η* resulting from softening of the high rank, low fluidity coal. It has also been confirmed that the η* of the resultant blend can be estimated from the η* of each component coal using a logarithmic additivity rule commonly employed for polymer blends. Polarised light microscopy has indicated that the degree of mixing between coals of different rank is minimal, with fusion restricted to the particle surface. It is therefore inappropriate to think of such a coal blend in the same way as a single coal, since each component coal behaves relatively independently. This limited fusion is important for understanding the coking pressure mechanism for blends. It is proposed here that the lower rank coal, which softens at lower temperature, is able to expand into the interparticle voids between the high rank coal that is yet to soften, and these voids can create channels for volatiles to traverse. Then, and importantly, when the high rank coal begins to expand, the pore structure developed in the resolidified structures of the low rank coal can facilitate removal of volatiles, while the resolidified material may also act as a suitable sorbent for volatile matter. This is considered to be the primary mechanism by which coal blending is able to alleviate coking pressure, and applies to addition of inert material also. Addition of a coal tar pitch was found to increase fluidity but also to extend the thermoplastic range to lower temperatures. This caused an increase in the swelling range, which was accompanied by a long plateau in η*, a feature which has previously been observed for certain high fluidity, high pressure coals. Elasticity and η* at the onset of expansion were also higher for both the pitch impregnated coals and the high pressure blends, which supports previous findings for singly charged high pressure coals, and confirms the potential use of such criteria for identifying potentially dangerous coals/blends.

On modeling the composition dependence of the bulk viscosity of immiscible polymer blends

AbstractThe purpose of this article is to clear the confusion in the literature on the following two issues: (1) determination of the bulk viscosity of immiscible polymer blends using a plunger‐type capillary viscometer and (2) modeling the composition dependence of the bulk viscosity of immiscible polymer blends. Related to the first issue, it is pointed out that measurement of the total pressure drop across the entire length of a capillary die, while using a plunger‐type viscometer, to determine the bulk viscosity of an immiscible polymer blend is not justified. This is because the morphology (the state of dispersion) of an immiscible polymer blend varies along the axis of a capillary die. Related to the second issue, it is pointed out that the use of such empirical expressions as inverse additivity or logarithmic additivity relationships is of no rheological significance to determine the composition dependence of the bulk viscosity of immiscible polymer blends. This is because such empirical expressions do not contain terms describing the state of dispersion of an immiscible polymer blend. A computational approach is suggested, though formidable but not insurmountable, which will lead to establishing rheology–morphology–processing relationships in immiscible polymer blends. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

On the addition of two incoherent unsteady noise records of different statistical structures

The present study is a follow-up of two previous studies of the second author in an attempt to understand the importance of the statistical structures of noise records in affecting that of the resultant noise records formed from their addition. The present results show that the difference in the shapes of the cumulative distributions of the combining noise records plays a dominant role in the process. It is also found that the commonly adopted logarithmic addition tends more to underestimate the L 10 instead of overestimating it as in the two previous studies regardless of the statistical structures of the noise records. The distributions of maximum over-estimation of the noise climate, the L 10 and the L 90 appear to be independent of the statistical structures and show insignificant diurnal variations.

Rheology of co‐continuous phase in physical thermoplastic elastomers

AbstractNowadays, chemical and physical thermoplastic elastomers have found many applications in different industries. Compatibilizer and co‐continuous composition are among the important factors which control the optimum properties of a number of physical blends. Morphology, mechanical and rheological properties of various blends of polystyrene (PS) and polybutadiene were investigated. The results show that the co‐continuous composition for these blends is located in‐between 24 and 35 wt% of PS. These blends show a negative deviation from the viscosity logarithmic additivity rule. This observation suggests an improvement in the interactions between the phases in co‐continuous composition. Rheological and mechanical properties were used in determination of the co‐continuous phase. Copyright © 2004 Society of Chemical Industry

On the addition of two incoherent unsteady noise records of similar statistical structures. Part 2: effects of long time span and diurnal variations

The present study is a follow-up of a previous investigation of the author in an attempt to understand how the statistical structures of noise records will affect that of the resultant noise record formed from their addition. This issue becomes particularly important when statistical indices such as L 10 and L 90 of the resultant noise record are required for planning or assessment purposes. Long time span sound pressure level records were obtained from 18 well-separated independent sites in the high-rise residential areas of Hong Kong. The results obtained from their addition are compared with those of the 25-min record addition done by the author previously. The diurnal variations of the addition results are also discussed. In general, the present results suggest that there is weak correlation between the long time span records. The currently adopted logarithmic addition procedure still over-estimates the noise climate and only limited improvement is found when compared to the results of the 25-min cases. The present results further confirm the importance of the noise statistical structures in the environmental noise impact assessment.

A Manual Slide Rule for Target-Controlled Infusion of Propofol: Development and Evaluation

We describe the development and evaluation of a simple slide rule that enables the bedside determination of the infusion rate for a particular target plasma concentration of propofol. The infusion rate to reach this target concentration at time (t) is the product of the target concentration, body weight, and a correction factor that depends on the time elapsed from the start of the initial infusion. Our target-controlled infusion (TCI) slide rule, constructed along this principle, performs the multiplications, analogous to the principle of the classical slide rule, as addition of logarithms. We calculated the percentage deviation of the predicted concentration obtained by STANPUMP versus predicted concentrations obtained using the infusion rates determined from the TCI slide rule. The evaluation using STANPUMP simulations showed, for a constant target concentration of 3 μg/mL of propofol, a mean deviation of 4.05% (max, 6.97%) in the first 15 min and a mean deviation of 0.5% (max, 2.03%) between 16 and 300 min. The mean deviation after changing the target from 3 μg/mL to 1, 2, 4, or 5 μg/mL ranged from 1.15% to 17.76%. This pocket-sized TCI slide rule combines the advantages of minimal financial and technical cost with reasonable accuracy.

On the addition of two incoherent unsteady noise records of similar statistical structures

Sixty four noise level recordings were carried out at building facades in the residential areas of Hong Kong in the present study. These records were then categorized into groups of different statistical structures using the Pearson frequency curve system. The effects of these statistical structures on the accuracy of predicting the statistical parameters of a record formed by the addition between any two noise records of similar statistical structures were examined. Results suggest that the currently adopted logarithmic addition tends to over-estimate the noise climates for bell-shaped noise level distributions, but it may also produce under-estimation for J-shaped ones. The worst deficiency of the logarithmic procedure appears for Pearson Type I(M) noise records which are commonly found in urban areas. Results also manifest the importance of noise level statistical structures in the noise impact assessments.