Similar Solution Structures Research Articles

Similar Constructing Method for Solving the Boundary Value Problem of the Compound Kummer Equation

This article is devoted to analyze the compound Kummer equation. Through the structure of left region and right region similarity kernel function, have similar structure of solution for this boundary value problems. The left field solution of this kind of boundary value problems can be obtained by combing the coefficients of boundary value problems on the left and the left area similar kernel function. The right field solution of this kind of boundary value problems can be expressed by assembling the left, the right area similar kernel function, the left lead solution functions and the coefficients of the convergence conditions. Thus put forward the simple method which was named similar constructive method to solve the boundary value problems of the compound Kummer equation. The put forward of this method provides the convenience for solving this kind of differential equation boundary value problems.

Similar Construction Method of the Boundary Value Problem of Composite Spherical Bessel Equations

Aimed at the boundary value problem of composite spherical Bessel equations. Through introducing similar kernel function in the left (right) region, the similar structure of solution was obtained. By analyzing the structure of solution, the solution in the left region was assembled by coefficient of left boundary value condition and similar kernel function in the left region, the solution in the right region was assembled by similar kernel function in the left (right) region; coefficient of left boundary value condition; left guide functions and coefficient of joint conditions. Thus a simple method of solving the boundary value problem of composite spherical Bessel equations is put forward, namely similar construction method; This method provides a way for solving boundary value problem of composite differential equations.

A Study about Solving the Nonlinear Spherical Seepage Model of Three-Area Composite Reservoir

This paper studies the nonlinear spherical seepage model of three-area composite reservoir under three kinds of outer boundary conditions (infinite boundary, constant pressure boundary and closed boundary) which not considering well-bore storage and skin factor. On the basis of similar structure of solution for differential equation’s boundary value problem, this paper obtains the solution of the nonlinear spherical seepage model of three-area composite reservoir. The study not only benefits to understand the inherent laws of the solution, but also provides the convenience to compile corresponding test software.

A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir

This study uses similar construction method of solution (SCMS) to solve mathematical models of fluid spherical flow in a fractal reservoir which can avoid the complicated mathematical deduction. The models are presented in three kinds of outer boundary conditions (infinite, constant pressure, and closed). The influence of wellbore storage effect, skin factor, and variable flow rate production is also involved in the inner boundary conditions. The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. The mathematical beauty of fractal is that the infinite complexity is formed with relatively simple equations. So the relation of reservoir parameters (wellbore storage effect, the skin factor, fractal dimension, and conductivity index), the formation pressure, and the wellbore pressure can be learnt easily. Type curves of the wellbore pressure and pressure derivative are plotted and analyzed in real domain using the Stehfest numerical invention algorithm. The SCMS and type curves can interpret intuitively transient pressure response of fractal spherical flow reservoir. The results obtained in this study have both theoretical and practical significance in evaluating fluid flow in such a fractal reservoir and embody the convenience of the SCMS.

Identification of two p23 co-chaperone isoforms in Leishmania braziliensis exhibiting similar structures and Hsp90 interaction properties despite divergent stabilities.

The small acidic protein called p23 acts as a co-chaperone for heat-shock protein of 90 kDa (Hsp90) during its ATPase cycle. p23 proteins inhibit Hsp90 ATPase activity and show intrinsic chaperone activity. A search for p23 in protozoa, especially trypanosomatids, led us to identify two putative proteins in the Leishmania braziliensis genome that share approximately 30% identity with each other and with the human p23. To understand the presence of two p23 isoforms in trypanosomatids, we obtained the recombinant p23 proteins of L. braziliensis (named Lbp23A and Lbp23B) and performed structural and functional studies. The recombinant proteins share similar solution structures; however, temperature- and chemical-induced unfolding experiments showed that Lbp23A is more stable than Lbp23B, suggesting that they may have different functions. Lbp23B prevented the temperature-induced aggregation of malic dehydrogenase more efficiently than did Lbp23A, whereas the two proteins had equivalent efficiencies with respect to preventing the temperature-induced aggregation of luciferase. Both proteins interacted with L. braziliensis Hsp90 (LbHsp90) and inhibited its ATPase activity, although their efficiencies differed. In vivo identification studies suggested that both proteins are present in L. braziliensis cells grown under different conditions, although Lbp23B may undergo post-translation modifications. Interaction studies indicated that both Lbp23 proteins interact with LbHsp90. Taken together, our data suggest that the two protozoa p23 isoforms act similarly when regulating Hsp90 function. However, they also have some differences, indicating that the L. braziliensis Hsp90 machine has features providing an opportunity for novel forms of selective inhibition of protozoan Hsp90.

A Study on Solving the Seepage Flow Model of Three-Area Composite Reservoir

This paper studies the seepage flow mathematical model of three-area composite reservoir under three kinds of outer boundary conditions (infinite boundary, constant pressure boundary and closed boundary), in which influences of well-bore storage and skin factor are not taken into consideration. On the basic of theory of similar structure of solution of boundary value problem of differential equation, this paper obtain the solution of the seepage flow model of three-area composite reservoir. The study is not only conducive to further analyze the inherent law of the solution and solve corresponding application problems, but also easy to compile corresponding analysis software.

Structural similarity between β3‐peptides synthesized from β3‐homo‐amino acids and aspartic acid monomers

Formation of stable secondary structures by oligomers that mimic natural peptides is a key asset for enhanced biological response. Here we show that oligomeric β(3)-hexapeptides synthesized from L-aspartic acid monomers (β(3)-peptides 1, 5a, and 6) or homologated β(3)-amino acids (β(3)-peptide 2), fold into similar stable 14-helical secondary structures in solution, except that the former form right-handed 14-helix and the later form left-handed 14-helix. β(3)-Peptides from L-Asp monomers contain an additional amide bond in the side chains that provides opportunities for more hydrogen bonding. However, based on the NMR solution structures, we found that β(3)-peptide from L-Asp monomers (1) and from homologated amino acids (2) form similar structures with no additional side-chain interactions. These results suggest that the β(3)-peptides derived from L-Asp are promising peptide-mimetics that can be readily synthesized using L-Asp monomers as well as the right-handed 14-helical conformation of these β(3)-peptides (such as 1 and 6) may prove beneficial in the design of mimics for right-handed α-helix of α-peptides.

회암사(檜巖寺) 수조명분(修造名分)의 변화와 종교적 해법의 유사구조 - 자장(慈藏)의 영향을 중심으로 -

The temple Hoeamsa(檜巖寺) was repaired by Naong(懶翁), and with this the power of the temple became far greater to be the greatest Buddhist temple during late Goryeo and early Joseon. Naong's reconstruction of Hoeamsa was originated from Jigong(指空)'s teaching 'Samsan Yangsu(三山兩水).' But it is not clear whether Samsan Yangsu really meant Hoeamsa. By the way, after 14 years, Naong suddenly remembered this word and began to repair Hoeamsa in a large scale. From this, we can guess that Naong tried to give the contemporary Buddhism some change through the repair of Hoeamsa. But, as King Gongmin(恭愍王) the greatest supporter of Naong was suddenly assassinated, the political situation changed a lot and Naong also died unexpectedly. Naong's death brought out the critical sense to Hoeamsa and, in the process to resolve the crisis, the repair of Hoeamsa began to be justified through diverse religious factors. As these were expanded and developed on and one, Hoeamsa came to be honored as the most divine temple in Korea during the early Joseon dynasty. Furthermore, into the cause structure for the Naong's repair of Hoeamsa, the influence of Jajang was added through Odaesan Buddhism. As we can well understand, late Silla situation of Jajang and the late Goryeo of Naong were very similar and the both Buddhist leaders should have derived out some religious solution for them. In other words, both of them had a similar recognition in finding the religious solution for the contemporary crises. It becomes a way to understand the Hoeamsa repairing structure taken by Naong and his disciples. Therefore, by comparing the similar religious solution structures given by Jajang and Naong and by clearer understanding on Samsan Yangsu spirit, we can see the repair of Hoeamsa and the related aspects more accurately.

A New Method and Applications of the Boundary Value Problem of Differential Equation

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

Protein NMR Structures Refined with Rosetta Have Higher Accuracy Relative to Corresponding X-ray Crystal Structures

We have found that refinement of protein NMR structures using Rosetta with experimental NMR restraints yields more accurate protein NMR structures than those that have been deposited in the PDB using standard refinement protocols. Using 40 pairs of NMR and X-ray crystal structures determined by the Northeast Structural Genomics Consortium, for proteins ranging in size from 5–22 kDa, restrained Rosetta refined structures fit better to the raw experimental data, are in better agreement with their X-ray counterparts, and have better phasing power compared to conventionally determined NMR structures. For 37 proteins for which NMR ensembles were available and which had similar structures in solution and in the crystal, all of the restrained Rosetta refined NMR structures were sufficiently accurate to be used for solving the corresponding X-ray crystal structures by molecular replacement. The protocol for restrained refinement of protein NMR structures was also compared with restrained CS-Rosetta calculations. For proteins smaller than 10 kDa, restrained CS-Rosetta, starting from extended conformations, provides slightly more accurate structures, while for proteins in the size range of 10–25 kDa the less CPU intensive restrained Rosetta refinement protocols provided equally or more accurate structures. The restrained Rosetta protocols described here can improve the accuracy of protein NMR structures and should find broad and general for studies of protein structure and function.

Similar Structure of Solution for Effective Wellbore Radius Model in the Spherical-Shaped Matrix of Dual-Porosity Reservoir

On the basis of percolation mechanism for dual-porosity, an effective wellbore radius model in the dual-porosity was established, and the Laplace space solution could be obtained by solving this model. The solution had a similar structure and could be simplified into a unified expression in the different outer boundary conditions. The solution with a similar structure can avoid the complex calculations, it is beneficial to analyze the influence of various parameters on the solution in the dual-porosity model, and facilitate to master and use by engineering technicians.

Similar Structure of Solution for the Model of Nonlinear Spherical Seepage in Composite Reservoir

The well testing model of nonlinear spherical percolation problems for composite reservoir is established under three different outer boundary conditions: closed boundary,constast pressure boundary,infinity boundary. the mathematical model are linearized by using variable substitution method, and then its solutions are derived by Laplace transform. According to the theory of similar structure of solutions to the differential equations, we obtain the similar structure of the solutions .The theory of similar structure is beneficial to understand the inherent laws of solutions and analyze the influence of parameters to solutions.

The Similar Structure of Solution in the Spherical Shaped Matrix of Dual-Porosity Reservoir Seepage Model

Aiming at spherical dual-porosity reservoir, an unsteady seepage model that based on the three different kinds of outer boundary (infinite, constant value and closed) conditions was established in this paper. Using the Laplace transform method, similar structure of dimensionless bottom pressure solution in the Laplace space and similar nuclear function were obtained. This is not only providing us a new road to further explore the inherent law of the solutions and compile corresponding analysis software, but also has a broad application prospects.

Similar Constructive Method for Solving a nonlinearly Spherical Percolation Model

In the view of nonlinear spherical percolation problem of dual porosity reservoir, a mathematical model considering three types of outer boundary conditions: closed, constant pressure, infinity was established in this paper. The mathematical model was linearized by substitution of variable and became a boundary value problem of ordinary differential equation in Laplace space by Laplace transformation. It was verified that such boundary value problem with one type of outer boundary had a similar structure of solution. And a new method: Similar Constructive Method was obtained for solving such boundary value problem. By this method, solutions with similar structure in other two outer boundary conditions were obtained. The Similar Constructive Method raises efficiency of solving such percolation model. DOI: http://dx.doi.org/10.11591/telkomnika.v11i3.2219 Full Text: PDF

Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow

On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porous media model under three kinds of outer boundary conditions (infinite, constant pressure, and closed), in which the influences of fractal dimension, spherical flow, skin effect, and storage are taken into consideration. And then we use SCMS to solve it. The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering.

The Solution Structure of Rabbit IgG Accounts for Its Interactions with the Fc Receptor and Complement C1q and Its Conformational Stability

Solution structures for antibodies are critical to understand function and therapeutic applications. The stability of the solution structure of rabbit IgG in different buffers and temperatures was determined by analytical ultracentrifugation and X-ray and neutron scattering. Rabbit IgG showed a principally monomeric species, which is well resolved from small amounts of a dimeric species. The proportion of dimer increased with increased concentration, decreased temperature and heavy water from 8% to 25% in all buffers except for high salt (250mM NaCl). The Guinier X-ray radius of gyration RG likewise increased with concentration in 137mM NaCl buffer but was unchanged in 250mM NaCl buffer. The Guinier neutron RG values increased as the temperature decreased. The X-ray and neutron distance distribution curves P(r) revealed two peaks, M1 and M2, whose positions did not change with concentration to indicate unchanged structures under all these conditions. The maximum dimension increased with concentration because of dimer formation. Constrained scattering modeling reproducibly revealed very similar asymmetric solution structures for monomeric rabbit IgG in different buffers, in which the Fab–Fc and Fab–Fab pairs were separated by maximally extended hinge structures. The dimer was best modeled by two pairs of Fab regions forming tip-to-tip contacts. The intact rabbit IgG structures explained the ability of its two ligands, the Fc receptor and complement C1q, to bind to the top of its Fc region that is fully accessible and unhindered by the Fab regions.

DETERMINING THE FOLDING DOMAIN OF LIPID FREE APOA-I IN SOLUTION BY MUTATION†

DETERMINING THE FOLDING DOMAIN OF LIPID FREE APOA-I IN SOLUTION BY MUTATION†

Oligo-m-aniline Foldamers

Nitrogen atoms showed intriguing properties such as, they can adopt sp2 or sp3 electronic configurations and form various degrees of conjugations with the adjacent aromatic rings depending on the electric nature of aromatic rings. Through deliberate combination of nitrogen atoms with aromatics of different electric nature, oligo-m-aniline foldamers were synthesized with a two-directional synthetic protocol. The synthesized hexamer and heptamer gave a snake-shape folding structure in the crystalline state. By means of 2D NOESY NMR experiments, both the hexamer and heptamer were found to adopt similar folding structures in solution as those in the solid state.

N-Terminal Domain of NMDA Receptors as Studied by LRET

NMDA Receptors, one of the three main classes of glutamate receptors that mediate excitatory transmission, are tetramers composed of glycine- binding (GluN1) subunits and glutamate- binding (GluN2) subunits. Allosteric regulators are known to bind to the amino-terminal domain of GluN2 subunits; specifically, zinc inhibits GluN2A and GluN2B subunits with varying efficacy. Luminescence resonance energy transfer (LRET) was used to study the soluble construct of the GluN2A and GluN2B amino-terminal domains. Donor and acceptor tags were attached through maleimide linkages to non-disulphide bonded cysteines introduced into lobes 1 and 2 of the bi-lobed amino-terminal domain structure. The LRET based distances of GluN2B are similar to the distances found in the crystal structure indicating that the protein adopts a similar structure in solution as in the crystal structure. Additionally, no significant change in the distance was observed upon addition of zinc, suggesting no significant changes in the average conformation of the bi-lobed protein upon binding zinc. Analogous measurements using the GluN2A amino-terminal domain revealed similar distance measurements to those observed in the GluN2B amino-terminal domain, suggesting a similar conformation of the GluN2A amino-terminal domain to that of the GluN2B amino- terminal domain. Additionally, a small decrease in the distance between the two lobes was observed upon addition of zinc suggesting a possible cleft- closure like conformational change in the GluN2A amino-terminal domain upon addition of saturating concentrations of zinc.

Phosphorescent Binuclear Iridium Complexes Based on Terpyridine–Carboxylate: An Experimental and Theoretical Study

The phosphorescent binuclear iridium(III) complexes tetrakis(2-phenylpyridine)μ-(2,2':6',2''-terpyridine-6,6''-dicarboxylic acid)diiridium (Ir1) and tetrakis(2-(2,4-difluorophenyl) pyridine))μ-(2,2':6',2''-terpyridine-6,6''-dicarboxylic acid)diiridium (Ir2) were synthesized in a straightforward manner and characterized using X-ray diffraction, NMR, UV-vis absorption, and emission spectroscopy. The complexes have similar solution structures in which the two iridium centers are equivalent. This is further confirmed by the solid state structure of Ir2. The newly reported complexes display intense luminescence in dichloromethane solutions with maxima at 538 (Ir1) and 477 nm (Ir2) at 298 K (496 and 468 nm at 77 K, respectively) and emission quantum yields reaching ~18% for Ir1. The emission quantum yield for Ir1 is among the highest values reported for dinuclear iridium complexes. It shows only a 11% decrease with respect to the emission quantum yield reported for its mononuclear analogue, while the molar extinction coefficient is roughly doubled. This suggests that such architectures are of potential interest for the development of polymetallic assemblies showing improved optical properties. DFT and time-dependent-DFT calculations were performed on the ground and excited states of the complexes to provide insights into their structural, electronic, and photophysical properties.