Polynomial algorithms for guillotine cutting of a rectangle into small rectangles of two kinds

In this paper the problem of optimally guillotine cutting a rectangle (A, B  ) into small rectangles of two kinds is considered. Rectangles of the first kind (c,_ai),i∈I$(c\text{,}{a}_i)\text{,}i\in I$ have the same width, and their heights can be various. Rectangles of the second kind (_bj,d),j∈J$(b_j\text{,}d)\text{,}j\in J$ have the same height, and their widths can be various. The number of occurrences of each small rectangle in a cutting pattern is not restricted. Similar problems often appear in the furniture industry. This cutting problem is reduced to the shortest path problem in a special rectangular grid, for which a linear time algorithm is suggested. This approach generalizes the approach of [E. Girlich, A.G. Tarnowski, On polynomial solvability of two multiprocessor scheduling problems, Mathematical Methods of Operations Research 50 (1999) 27–51; A.G. Tarnowski, Advanced polynomial time algorithm for guillotine generalized pallet loading problem, in: The International Scientific Collection: Decision Making Under Conditions of Uncertainty (Cutting-Packing Problems), Ufa State Aviation Technical University, 1997, pp. 93–124] and allows us to construct polynomial algorithms for the guillotine cutting problem considered with a fixed number of small rectangles of two kinds.     

Nonradiative energy transfer in mixed Langmuir monolayers and Langmuir–Blodgett films of compounds of different chemical composition and structure

Russian Chemical Bulletin - The efficiency of the Förster resonance energy transfer (FRET) in a monolayer film containing the energy donor and energy acceptor fluorophores is low since the...     

Modification of microcrystalline cellulose by a binary mixture of pyromellitic dianhydride and phosphoric acid

The reactions involved in the esteriification of microcrystalline cellulose with a binary mixture of pyromellitic dianhydride and phosphoric acid have been studied. By changing the molar ratio of dianhydride to acid it is possible to regulate the course of the reaction and to obtain products with required contents of phosphoric acid and carboxy groups.Tashkent Institute of Chemical Technology, 700034, Tashkent, ul. Shevchenko, 1. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 583–586, July–August, 1996. Original article submitted January 22, 1996.     

Optical parametric oscillator based off-axis integrated cavity output spectroscopy for rapid chemical sensing

An optical parametric oscillator (OPO), pumped by a fiber-amplified diode laser, is combined with off-axis integrated cavity output spectroscopy (OA-ICOS). The cw OPO (power 1.2 W, tunability 3-4 μm, 5 cm(-1) mode-hop-free tuning) has a tuning speed of 100 THz/s, which is ideal for rapid and sensitive trace gas detection. Combined with OA-ICOS, a detection limit of 50 parts per trillion by volume (1×10(12)) of ethane (C(2)H(6)) in nitrogen was obtained in 0.25s at 2997 cm(-1), corresponding to a noise equivalent absorption sensitivity of 4.8×10(-11) cm(-1) Hz(-1/2). The system demonstrates real-time measurements of methane and water in exhaled human breath.     

Magnetic properties of dilute magnetic semiconductor Cd<Subscript>0.82</Subscript>Mn<Subscript>0.18</Subscript>GeAs<Subscript>2</Subscript> under high pressures

We have studied the effect of high pressures on the electrical and magnetic properties of dilute magnetic semiconductor Cd_0.82Mn_0.18GeAs₂. Electrical resistivity, Hall coefficient, transverse and longitudinal magnetic resistance, and magnetic susceptibility have been measured under high pressures (up to 9 GPa). The energy of a manganese impurity level was estimated at 155 meV from electrical resistivity and Hall factor versus temperature curves at the atmospheric pressure. Structural and magnetic phase transitions have been discovered in Hall resistance versus magnetic field curves measured at various temperatures; abnormal and normal Hall factors have been calculated.     

Electrophysical Properties of ZnAs 2 and CdAs 2 at Hydrostatic Pressure up to 9 GPa

Specific electroresistance and Hall coefficient on oriented ZnAs 2 and CdAs 2 single crystals in the region of room temperatures at hydrostatic pressure up to 9 GPa were measured. In p -ZnAs 2 specific electroresistance falls for one order of magnitude with the increase of pressure, and Hall coefficient falls for two orders in magnitude, and at P =7 GPa specific electroresistance and Hall coefficient come out to a saturation. Under mentioned conditions the phase transition in investigated p -ZnAs 2 samples was not observed, in all probability it occurs under the pressure P >10 GPa. Two groups of n -CdAs 2 samples oriented on [1 0 0] and [0 0 1] directions were investigated. The reversible structural phase transition was observed in investigated n -CdAs 2 samples at P =5.5 GPa from the dependencies of specific electroresistance 𝜌 ( P ) and Hall coefficient R H ( P ). On the basis of the values of concentrations and mobilities before and after phase transition a conclusion was made that semiconductor-semiconductor transition takes place in n -CdAs 2 . Maxima that earlier weren't observed, were detected on dependencies 𝜌 ( P ), R H ( P ) at P =1.8 GPa and at P =3 GPa.     

Electron and magnetic transport in the diluted magnetic semiconductor CdGeAs2<Mn>at high pressures

In CdGeAs₂<Mn>, a metamagnetic phase transition and a negative magnetic resistance induced by high pressure were found and studied.     

Definable relations in Turing degree structures

In this paper we investigate questions about the definability of classes of n-computably enumerable (c. e.) sets and degrees in the Ershov difference hierarchy. It is proved that the class of all c. e. sets is definable under the set inclusion ? in all finite levels of the difference hierarchy. It is also proved the definability of all m-c. e. degrees in each higher level of the hierarchy. Besides, for each level n, n ≥ 2, of the hierarchy a definable non-trivial subset of n-c. e. degrees is established.     

Structure-Dependent Magnetoresistance in the Zn<Subscript>0.1</Subscript>Cd<Subscript>0.9</Subscript>GeAs<Subscript>2</Subscript> + MnAs Hybrid Nanocomposite

The effect of high pressure on electron transport and on the field dependence of the transverse magnetoresistance has been studied in a hybrid nanocomposite based on the Zn0.1Cd0.9GeAs2 matrix and MnAs clusters. A record high negative magnetoresistance of ~74% is formed near a pressure-induced structural transition (P≈ 3.5 GPa). The considered scattering mechanisms include both the contribution from MnAs clusters at relatively low pressures (up to 0.7 GPa) and spin-dependent scattering by localized magnetic moments in the Mn-substituted structure of the matrix in the region of the structural transition. The presence of the positive magnetoresistance region associated with the two-band transport model in the high-pressure phase, as well as the large negative magnetoresistance, is described in the framework of the semiempirical Khosla–Fischer expression.