Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Peculiarities of microwave discharge between a copper pin electrode and technical water

© 2014, Pleiades Publishing, Ltd. Some experimental results on burning of the microwave discharge between a copper pin electrode and technical water, in air, are presented within the ranges of the voltage U = 28–75 kV, the frequency f = 40–100 MHz, and the interelectrode space l = 2–20 mm. The essential influence of the pulse repetition frequency and the interelectrode space on the development, the shape, and the structure of the microwave discharge between the copper electrode and the technical water is revealed. Also the transition of the weakly glowing microdischarges inside the microwave discharge into the multichannel spark discharge is revealed. A temperature decrease below room temperature in the interelectrode gap of the microwave discharge with the technical water is discovered

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

Применение МРТ-последовательности DIXON в диагностике изменений губчатого вещества тел позвонков в сопоставлении с данными остеоденситометрии

The aim of this study was to analyze the patterns of changes in the fat fraction of the vertebral bodies according to the modified DIXON protocol (mDixon, MRI) in patients of different age groups with densitometry data.Materials and methods. In the course of our study, a Siemens Magnetom Verio 3T tomograph was used for diagnostics, for assessing the condition of the vertebrae of the lumbosacral spine, measuring FF, a computer program was used: “RadiAnt DICOM viewer”. DIXON (two-point) parameters of TSE pulse train with T2 type of weighting: TR 4000 ms, TE 88 ms, slice thickness 4 mm, matrix 320 × 320, NEX 1, FOV 260 × 260 mm, pixel size 0.8 × 0.8 mm, bandwidth 345 Hz/pixel. Scanning time: 3 min. 50 sec. We also used a GE Lunar Prodigy densitometer. Measurement parameters: mode – standard (13–25 cm), length 19.1 cm, width 18.0 cm. Method: mDixon.Results. 71 patients were examined (average age is 57 years; average BMI (body mass index): 27.94). Osteopenia was diagnosed in 21 patients, osteoporosis – in 13. Bone mineral density (BMD) was obtained using X-ray densitometry, which served as a reference for detecting abnormal bone density and osteoporosis. A comparison was made of BMD values in patients with normal and patients with osteoporosis / osteopenia: the values in patients with normal were 21.85% higher than in patients with osteoporosis / osteopenia. We also compared the parameters of vertebral fat density (FF) in patients with normal and pathology – the values in patients with normal were 15.65% less than in patients with pathology. Correlation analysis revealed a relationship between BMD and FF parameters. According to the results of the morphometry of the vertebral bodies, wedge-shaped deformity of the vertebral bodies was revealed in 8% of patients with osteoporosis / osteopenia.Conclusions. The MRI method based on the DIXON trace is of great importance in the diagnosis of changes in the spongy substance of the vertebral bodies. In the study of correlation analysis, an inverse relationship was found between the BMD and FF parameters.Цель исследования: анализ закономерностей изменения жировой фракции тел позвонков по данным модифицированного протокола DIXON (mDixon, МРТ) у пациентов различных возрастных групп в сопоставлении с данными денситометрии.Материал и методы. Для диагностики был использован томограф Siemens Magnetom Verio 3 Tл, для оценки состояния позвонков пояснично-крестцового отдела позвоночника, измерения жировой фракции (FF – fat fraction) была использована компьютерная программа: RadiAnt DICOM viewer. Параметры DIXON (two-point) импульсной последовательности TSE с Т2-типом взвешенности: TR 4000 мс, TE 88 мс, толщина среза 4 мм, матрица 320 × 320, NEX 1, FOV 260 × 260 мм, размер пикселя 0,8 × 0,8 мм, полоса пропускания 345 Гц/пиксель. Время сканирования фиксировано и составило 3 мин 50 с. Также в работе был использован денситометр GE Lunar Prodigy. Выставленные параметры измерения: режим – стандарт (13–25 см), длина 19,1 см, ширина 18,0 см. Метод: mDixon.Результаты. Всего был обследован 71 пациент (средний возраст 57 лет; средний ИМТ составил 27,94). Остеопения была диагностирована у 21 больного, остеопороз – у 13. Минеральная плотность кости (BMD) была получена с помощью рентгеновской денситометрии, которая служила методом для выявления аномальной плотности кости и остеопороза. Было сделано сравнение значений BMD у пациентов с нормой и пациентов с остеопорозом/остеопенией: значения у пациентов с нормой были на 21,85% больше, чем у пациентов с остеопорозом/остеопенией. Также было проведено сравнение параметров FF у пациентов с нормой и патологией – значения у пациентов с нормой были на 15,65% меньше, чем у пациентов с патологией. При проведении корреляционного анализа была выявлена зависимость между параметрами BMD и FF. По результатам морфометрии тел позвонков в 8% случаев у пациентов с остеопорозом / остеопенией была выявлена клиновидная деформация тел позвонков.Выводы. Метод МРТ-последовательности DIXON является важным звеном в диагностике изменений губчатого вещества тел позвонков. При исследовании корреляционного анализа была выявлена обратная зависимость между параметрами BMD и FF

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

The formation of human populations in South and Central Asia

By sequencing 523 ancient humans, we show that the primary source of ancestry in modern South Asians is a prehistoric genetic gradient between people related to early hunter-gatherers of Iran and Southeast Asia. After the Indus Valley Civilization’s decline, its people mixed with individuals in the southeast to form one of the two main ancestral populations of South Asia, whose direct descendants live in southern India. Simultaneously, they mixed with descendants of Steppe pastoralists who, starting around 4000 years ago, spread via Central Asia to form the other main ancestral population. The Steppe ancestry in South Asia has the same profile as that in Bronze Age Eastern Europe, tracking a movement of people that affected both regions and that likely spread the distinctive features shared between Indo-Iranian and Balto-Slavic languages

Experimental characterisation of textile compaction response: A benchmark exercise

This paper reports the results of an international benchmark exercise on the measurement of fibre bed compaction behaviour. The aim was to identify aspects of the test method critical to obtain reliable results and to arrive at a recommended test procedure for fibre bed compaction measurements. A glass fibre 2/2 twill weave and a biaxial (±45°) glass fibre non-crimp fabric (NCF) were tested in dry and wet conditions. All participants used the same testing procedure but were allowed to use the testing frame, the fixture and sample geometry of their choice. The results showed a large scatter in the maximum compaction stress between participants at the given target thickness, with coefficients of variation ranging from 38% to 58%. Statistical analysis of data indicated that wetting of the specimen significantly affected the scatter in results for the woven fabric, but not for the NCF. This is related to the fibre mobility in the architectures in both fabrics. As isolating the effect of other test parameters on the results was not possible, no statistically significant effect of other test parameters could be proven. The high sensitivity of the recorded compaction pressure near the minimum specimen thickness to changes in specimen thickness suggests that small uncertainties in thickness can result in large variations in the maximum value of the compaction stress. Hence, it is suspected that the thickness measurement technique used may have an effect on the scatter