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In this work, we study the spectral property of generalized Sierpinski-type self-affine measures μ M , D on R 2 generated by an expanding integer matrix M ∈ M 2 ( Z ) with det ⁡ ( M ) ∈ 3 Z and a non-collinear integer digit set D = { ( 0 , 0 ) t , ( α 1 , α 2 ) t , ( β 1 , β 2 ) t } with α 1 β 2 − α 2 β 1 ∈ 3 Z . We give the sufficient and necessary conditions for μ M , D to be a spectral measure, i.e., there exists a countable subset Λ ⊂ R 2 such that E ( Λ ) = { e 2 π i 〈 λ , x 〉 : λ ∈ Λ } forms an orthonormal basis for L 2 ( μ M , D ) . This completely settles the spectrality of the self-affine measure μ M , D .

Fluid inhomogeneous distribution affects heat transfer efficiency in the plate-fin heat exchanger (PFHE). In order to improve fluid uniform distribution in the exchanger, the irregular-shaped hole leading flow structure (IHLFS) was proposed for solving fluid inhomogeneous distribution among different layers of PFHE. The inlet distributor with irregular-shaped holes was designed according to different inlet flow velocities aiming at improving fluid uniform distribution. The results on fluid flow and heat transfer characteristics were carried out by the methods of CFD and experimental analysis, and finally, the fluid flow characteristics in inlet section of PFHE with IHLFS were achieved. Comparing with round hole leading flow structure (RHLFS), it can be observed that fluid distribution in PFHE with IHLFS is more uniform than that with round hole, however, the dynamic pressure increases accordingly and finally, increases the ratio of heat transfer and dynamic pressure. The comparison results also demonstrate that the IHLFS can improve fluid distribution, decrease fluid impact in inlet section of PFHE and finally, improve heat transfer enhancement.

Let the iterated function systems { S i } i = 1 N \{S_{i}\}_{i=1}^{N} be defined by S i ⁢ ( x ) = ( - 1 ) i - 1 ⁢ ρ ⁢ ( x + d i ) S_{i}(x)=(-1)^{i-1}\rho(x+d_{i}) , x ∈ R x\in\mathbb{R} , d i ∈ D d_{i}\in D , where 0 < ρ < 1 0 , and 𝐷 is a finite subset of ℤ. Let the measure μ ρ , P \mu_{\rho,P} be generated by the IFS and the probability weight P = { p i } i = 1 N P=\{p_{i}\}_{i=1}^{N} . In this paper, we introduce a new way to consider the spectrality of μ ρ , P \mu_{\rho,P} , and obtain a sufficient and necessary condition for N = 2 N=2 , and construct two examples of spectral measures for N = 2 ⁢ L ≥ 4 N=2L\geq 4 and N = 2 ⁢ L + 1 N=2L+1 , respectively.

In this work, we study the non-spectrality of the self-affine measure μ M , D {\mu_{M,D}} generated by an expanding integer matrix M ∈ M 2 ⁢ ( ℤ ) {M\in M_{2}(\mathbb{Z})} with det ⁡ ( M ) ∉ 2 ⁢ ℤ {\det(M)\notin 2\mathbb{Z}} and the integer digit set D = { ( 0 , 0 ) t , ( α 1 , α 2 ) t , ( β 1 , β 2 ) t , ( - α 1 - β 1 , - α 2 - β 2 ) t } D=\bigl{\{}(0,0)^{t},(\alpha_{1},\alpha_{2})^{t},(\beta_{1},\beta_{2})^{t},(-% \alpha_{1}-\beta_{1},-\alpha_{2}-\beta_{2})^{t}\bigr{\}} with α 1 ⁢ β 2 - α 2 ⁢ β 1 ≠ 0 {\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1}\neq 0} . Let η = max ⁡ { s : 2 s | ( α 1 ⁢ β 2 - α 2 ⁢ β 1 ) } {\eta=\max\{s:2^{s}|(\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1})\}} . We show that if 0 ≤ η ≤ 2 {0\leq\eta\leq 2} , then L 2 ⁢ ( μ M , D ) {L^{2}(\mu_{M,D})} contains at most 2 2 ⁢ ( η + 1 ) {2^{2(\eta+1)}} mutually orthogonal exponential functions, and the number 2 2 ⁢ ( η + 1 ) {2^{2(\eta+1)}} is the best. However, the number is strictly less than 2 2 ⁢ ( η + 1 ) {2^{2(\eta+1)}} if η ≥ 3 {\eta\geq 3} , and it is related to the order of the matrix M.

Convenient and green methods to synthesize highly efficient and stable multi-functional electrode materials are the key and a challenge for the industrial application of new energy conversion devices. Herein, we have developed a general host–guest strategy to construct amorphous hetero-atom doped cobalt phosphates; in the first step, we fast synthesized large-scale 2D Co-based phosphate precursors with different organic amine guest molecules by a hydrothermal method, afterwards, we calcined these precursors at different annealing temperatures, leading to the decomposition of organic guest molecules, and consequently, we obtained amorphous C,N co-doped mesoporous Co-based phosphates during this decomposition process. Moreover, the optimal C4NCPO-450 shows bi-functional activity for the Oxygen Evolution Reaction (OER) and supercapacitor applications. Which has a low overpotential of 292 mV and a Tafel slope of 67.45 mV dec−1 for the OER, and when used as an electrode material for supercapacitors, it reveals a large specific capacitance of 326 F g−1@1 A g−1, accompanied by a stability of 2200 charge and discharge cycles. We suppose that this method can be used to prepare other hetero-atom doped mesoporous electrode materials, which should be promising candidates in the electrochemical energy storage and conversion field.

Let the self-affine measure μ M , D {\mu_{M,D}} be generated by an expanding real matrix M = diag ⁡ ( ρ 1 - 1 , ρ 2 - 1 ) {M=\operatorname{diag}(\rho_{1}^{-1},\rho_{2}^{-1})} and an integer digit set D = { ( 0 , 0 ) t , ( α 1 , α 2 ) t , ( β 1 , β 2 ) t } {D=\{(0,0)^{t},(\alpha_{1},\alpha_{2})^{t},(\beta_{1},\beta_{2})^{t}\}} with α 1 ⁢ β 2 - α 2 ⁢ β 1 ≠ 0 {\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1}\neq 0} . In this paper, the sufficient and necessary conditions for L 2 ⁢ ( μ M , D ) {L^{2}(\mu_{M,D})} to contain an infinite orthogonal set of exponential functions are given.

Let $\{M_{n}\}_{n=1}^{\infty }$ be a sequence of expanding matrices with $M_{n}=\operatorname{diag}(p_{n},q_{n})$, and let $\{{\mathcal{D}}_{n}\}_{n=1}^{\infty }$ be a sequence of digit sets with ${\mathcal{D}}_{n}=\{(0,0)^{t},(a_{n},0)^{t},(0,b_{n})^{t},\pm (a_{n},b_{n})^{t}\}$, where $p_{n}$, $q_{n}$, $a_{n}$ and $b_{n}$ are positive integers for all $n\geqslant 1$. If $\sup _{n\geqslant 1}\{\frac{a_{n}}{p_{n}},\frac{b_{n}}{q_{n}}\}, then the infinite convolution $\unicode[STIX]{x1D707}_{\{M_{n}\},\{{\mathcal{D}}_{n}\}}=\unicode[STIX]{x1D6FF}_{M_{1}^{-1}{\mathcal{D}}_{1}}\ast \unicode[STIX]{x1D6FF}_{(M_{1}M_{2})^{-1}{\mathcal{D}}_{2}}\ast \cdots \,$ is a Borel probability measure (Cantor–Dust–Moran measure). In this paper, we investigate whenever there exists a discrete set $\unicode[STIX]{x1D6EC}$ such that $\{e^{2\unicode[STIX]{x1D70B}i\langle \unicode[STIX]{x1D706},x\rangle }:\unicode[STIX]{x1D706}\in \unicode[STIX]{x1D6EC}\}$ is an orthonormal basis for $L^{2}(\unicode[STIX]{x1D707}_{\{M_{n}\},\{{\mathcal{D}}_{n}\}})$.

The application of NiCo-LDHs as electrode materials for supercapacitors has attracted widespread attention. However, pristine NiCo-LDHs always suffer from low conductivity and instability that limit their electrochemical performance in supercapacitors. Herein, we rationally engineered a novel KCu7S4@NiCo-LDH core–shell structure with good capacitive performance using a simple one-step solvothermal method and applied this structure as an electrode material for supercapacitors. KCu7S4 nanowires act as a dependable “skeleton” for supporting the NiCo-LDH nanosheets, thus preventing the aggregation of NiCo-LDHs and improving their conductivity. By controlling the reaction time and the ratio of Ni/Co in the precursor solution, according to the results of electrochemical testing, an optimal composite was obtained with Ni/Co = 2/1 and the reaction time of 8 h; the final KCu7S4@Ni2Co1-LDH composite possessed the high specific capacitance of 1104.5 F g−1 (122.7 mA h g−1) at 2 A g−1, good rate capability of 65.9% when the current density reached up to 10 A g−1, and a long-term stability (an 83.5% capacitance retention after 1000 cycles).

Under some supportive evidences of known results about non-spectral self-affine measures, Li proposed a conjecture in [18] (J. Funct. Anal. 255, 2008), which is so-called “non-spectral conjecture”. In this paper, we prove that Li's non-spectral conjecture is true under some suitable condition.

In this paper, we consider the spectral properties of self-similar measures μ R , D generated by the integer R = N q and the product-form digit set D = { 0 , 1 , … , N − 1 } ⊕ N p { 0 , 1 , … , N − 1 } , where the integers q , p ≥ 1 and N ≥ 2 . We show that μ R , D is a spectral measure if and only if q ∤ p .

The fluid-structure interaction performance of plate-fin heat exchanger (PFHE) with serrated fins in large scale air-separation equipment was investigated in this paper. The stress and deformation of fins were analyzed, besides, the interaction equations were deduced by Galerkin method. The governing equations of fluid flow and heat transfer in PFHE were deduced by finite volume method (FVM). The distribution of strain and stress were calculated in large scale air separation equipment and the coupling situation of serrated fins under laminar situation was analyzed. The results indicated that the interactions between fins and fluid flow in the exchanger have significant impacts on heat transfer enhancement, meanwhile, the strain and stress of fins includes dynamic pressure of the sealing head and flow impact with the increase of flow velocity. The impacts are especially significant at the conjunction of two fins because of the non-alignment fins. It can be concluded that the soldering process and channel width led to structure deformation of fins in the exchanger, and degraded heat transfer efficiency.

We study spectral properties of the self-affine measure μ M , D generated by an expanding integer matrix M ∈ M n ( Z ) and a consecutive collinear digit set D = { 0 , 1 , … , q − 1 } v where v ∈ Z n ∖ { 0 } and q ≥ 2 is an integer. Some sufficient conditions for μ M , D to be a spectral measure or to have infinitely many orthogonal exponentials are given. Moreover, for some special cases, we can obtain a necessary and sufficient condition on the spectrality of μ M , D . Our study generalizes the one dimensional results proved by Dai, et al. [4] , [5] .

Let the self-similar measure [Formula: see text] be generated by an expanding real matrix [Formula: see text] and a digit set [Formula: see text] in space [Formula: see text]. In this paper, we only consider [Formula: see text] and the case [Formula: see text] is similar. We show that there exists an infinite orthogonal set of exponential functions in [Formula: see text] if and only if [Formula: see text] for some [Formula: see text] with [Formula: see text]. Furthermore, for the cases that [Formula: see text] does not admit any infinite orthogonal set of exponential functions, the exact cardinality of orthogonal exponential functions in [Formula: see text] is given.

In this paper, we consider the planar self-affine measures $\mu_{M,D}$ generated by an expanding matrix $M\in M_2(\mathbb{Z})$ and an integer digit set $ D=\left\{ {\left( {\begin{array}{*{20}{c}} 0\\ 0 \end{array}} \right),\left( {\begin{array}{*{20}{c}} \alpha_1\\ \alpha_2 \end{array}} \right),\left( {\begin{array}{*{20}{c}} \beta_1\\ \beta_2 \end{array}} \right)} \right\} $ with $\alpha_1\beta_2-\alpha_2\beta_1\neq0$. We show that if $\det(M)\notin 3\mathbb{Z}$, then the mutually orthogonal exponential functions in $L^2(\mu_{M,D})$ is finite, and the exact maximal cardinality is given.

The aim of this study was to analyze the long-term efficacy and safety of angiotensin-converting enzyme inhibitor (ACEi) and ACEi + angiotensin receptor blocker (ARB) treatments in a cohort of children with Alport syndrome (AS). This was a respective review of 79 Chinese children with AS who received ACEi alone or combined ACEi + ARB therapy. The mean age of the pediatric patients with AS at onset of treatment was 8.6 ± 4.1 (range 1.5–16.3) years. The mean duration of follow-up was 2.5 ± 1.8 (range 0.5–7.8) years. For analysis, we separated the children into three groups according to proteinuria level before treatment, namely

Fin arrangement, which can cause temperature to be distributed non-uniformly and decrease heat exchange efficiency, can also affect fluid flow and distribution in different channels of a plate-fin heat exchanger. To reduce fluid maldistribution, the fluid flow and distribution should be investigated systematically. However, there is as yet no research reported on the fin ar- rangement effect. We investigated fluid flow and heat transfer at the inlet of a plate-fin heat exchanger by numerical calculation combined with simulation analysis. We simulated the fluid flow under seven kinds of fin arrangement, and analyzed the effects. The distribution of fluid parameters in four monitor positions among three sections was examined when the inlet flow velocity was 1 m/s with an inlet structure arranged with different numbers of fins. Denser fin arrangements among inlet, diversion, and heat exchange sections all intensify the turbulence at the outlet. With increase of arrangement density, the fluid flow direction will be changed and the fluid distribution inside the exchanger will be intensified to equalize the fluid temperature in different channels of the same layer. Furthermore, the effects of 18 combinations of fins in different sections on fluid flow were studied. Fin arrange- ments in different sections have more significant effect on turbulence than flow velocity and pressure; in comparison with the inlet and heat exchange sections, the diversion section has a significant effect on turbulence at the outlet of the heat exchanger.

Hexangular in-phase coherently coupled arrays of vertical cavity surface-emitting lasers (VCSELs) were fabricated using proton implantation. The arrays show excellent beam quality with far-field divergence of 4.8° and the output power of 3mW under continuous-wave condition. Different global flower-shaped patterns appeared with the varied injection currents.

In this paper, we consider the non-spectrality of the planar self-affine measures [Formula: see text] generated by an expanding integer matrix [Formula: see text] and a four-element digit set [Formula: see text] We show that [Formula: see text] contains an infinite orthogonal set of exponential functions if and only if [Formula: see text]. Moreover, if [Formula: see text], then there exist at most [Formula: see text] mutually orthogonal exponential functions in [Formula: see text], and the number [Formula: see text] is the best.

For the self-affine measures [Formula: see text] generated by a diagonal matrix [Formula: see text] with entries [Formula: see text] and the digit set [Formula: see text], Li showed that there exists an infinite orthogonal exponential functions set in [Formula: see text] if and only if at least two of the three numbers [Formula: see text] are even, and conjectured that there exist at most four mutually orthogonal exponential functions in [Formula: see text] for other cases [J.-L. Li, Non-spectrality of self-affine measures on the spatial Sierpinski gasket, J. Math. Anal. Appl. 432 (2015) 1005–1017]. This conjecture was disproved by Wang and Li through constructing a class of the eight-element orthogonal exponential functions [Q. Wang and J.-L. Li, There are eight-element orthogonal exponentials on the spatial Sierpinski gasket, Math. Nachr. 292 (2019) 211–226]. In this paper, we will show that there are any number of orthogonal exponential functions in [Formula: see text] if two of the three numbers [Formula: see text] are different odd and the other is even.

For an analytic function f on the open unit disk D and continuous on D ¯ , the Cantor boundary behavior (CBB) is used to describe the curve f ( ∂ D ) that forms infinitely many fractal-look loops everywhere. The class of analytic functions with the CBB was formulated and investigated in Dong et al. [6] . In this note, our main objective is to give further discuss of the criteria of CBB in Dong et al. [6] . We show that the two major criteria, the accumulation of the zeros of f ′ ( z ) near the boundary and the fast mean growth rate of f ′ ( z ) near the boundary, do not imply each other. Also we make an improvement of another criterion, which allows us to have more examples of CBB.

In this paper, we consider the non-spectral problem for the planar self-affine measures $\mu_{M,D}$ generated by an expanding integer matrix $M\in M_2(\mathbb{Z})$ and a finite digit set $D\subset\mathbb{Z}^2$. Let $p\geq2$ be a positive integer, $E_p^2:=\frac{1}{p}\{(i,j)^t:0\leq i,j\leq p-1\}$ and $\mathcal{Z}_{D}^2:=\{x\in[0, 1)^2:\sum_{d\in D}{e^{2\pi i\langle d,x\rangle}}=0\}$. We show that if $\emptyset\neq\mathcal{Z}_{D}^2\subset E_p^2\setminus\{0\}$ and $\gcd(\det(M),p)=1$, then there exist at most $p^2$ mutually orthogonal exponential functions in $L^2(\mu_{M,D})$. In particular, if $p$ is a prime, then the number $p^2$ is the best., Comment: 14 pages

During oil well production, it was a serious phenomenon of wax deposition on the parts such as oil production system section break.For the fluid flow problem of the collar in sucker rod, the research of this thesis applies Flunt software to perform numerical simulation of the flow conditions under different outputs, and presents relevant velocity vector and velocity nephogram of the crude oil at the collar in sucker rod. Through analysis, it was believed that the wax deposition could not be efficiently settled only by high fluid velocity raised by output increase, and the relevant technical measures were proposed to prevent wax deposition, providing the theoretical thesis for paraffin removal and control at oil well.

Violation of discipline by students may have a direct impact on the school spirit and academic atmosphere construction of colleges and universities and is becoming a hot issue which is brought to public attention. Survey and analysis have been conducted on violation of discipline by students of Petroleum and Natural Gass Engineering College from such three aspects as type of discipline violation, type of punishment as well as education background of students being punished so as to better adapt to the student management work under new situation and timely and accurately grasp the trend of student discipline violation in current stage. The paper aims to analyze and explore the reasons of discipline violation by students of Petroleum and Natural Gass Engineering College and its inherent law through deep analysis on both subjective factors and objective factors leading to disciplinary offence. Corresponding precautionary measures and countermeasures have been put forward to reduce and even avoid the occurrence of disciplinary offence by students.

The cementing quality is directly related to the normal operation of the gas well, therefore, the evaluation of cementing quality is key to the correctly use the gas well as well as to take measures to protect the gas well. In this paper, four first wave amplitudes at the same depth point when using the borehole compensated sonic logger with double transceiver technique to carry out the acoustic amplitude log operation are served as the discriminant factors to evaluate the cementing quality. Taking the engineering actual measured data as the learning samples and using the particle swarm optimization to optimize the parameters of support vector machine, this paper established the intelligent evaluation model for cementing quality based on genetic algorithm (GA) and support vector machine (SVM). The model employs the excellent characteristic of SVM which has high speed of solving and could describe nonlinear relation as well as the characteristic of GA which has global optimization. Through test of engineering samples, the research result showed that this model has fast astringency and high precision, providing a new method and approach for the fast and accurate evaluation of the well cementing quality.

Finding the right abandoned well (or new drilling ) leakage layer reinjection into the ground is the most effective, the most mature, the most commonly used method in the gas filed water treatment. By simplifying assumptions and the establishment of mathematical model and FEM, simulation and calculation of stress status of the tubing and casing, Analysis of wellbore integrity, for the analysis of the wellbore risk of gas field water reinjection wells and reinjection wells safety operation provide important theoretical support.

The construction of practice teaching base on campus which is close to the front of production line and which can reflect the real environments of oil fields is an important condition to train applied and high skilled talents of petroleum engineering major. This paper, by combining the requirements for practice teaching base for the construction of petroleum engineering major, summarizes the construction targets of practice teaching base for petroleum engineering, and further puts forward the idea and principle of constructing the practice teaching base, analyzes the functions which shall be met for practice teaching base for petroleum engineering and discusses the construction mode of practice teaching base.

The necessity on construction for practical teaching base on campus for petroleum engineering is described from such three aspects as requirement of practical talents training, requirement of vocational skills training as well as requirement of subject construction and campus culture construction in this article, the construction mode of practical teaching base on campus for petroleum engineering is discussed and the advantage of establishing the practical teaching base on campus cooperated jointly by campus and enterprise is analyze. Finally, the efficiency produced by the practical teaching on campus is summarized with combination of the operation condition of practical teaching base on campus for petroleum engineering.

It is very important to forecast the gas well productivity of gas reservoir accurately. On the basis of analyzing the parameter performance of support vector machine (SVM) for regression estimation, the paper proposes gas well productivity prediction model based on particle swarm optimization (PSO) and SVM. The parameter of SVM was optimized by PSO. This method took advantage of the minimum structure risk of SVM and the quickly globally optimizing ability of PSO. Compared with BP neural network model, the proposed GA-SVM model for gas well productivity in practical engineering has higher accuracy and speed, and the maximum error is 2.8% . Thus, it provided a new approach to predict the gas well productivity.

Emergency capability is the key to control the development of gas pipeline, reduce the social loss, and protect the safety of city.city gas pipeline emergency capability evaluation index system is set up. The weight of the evaluation index would be analyzed by analytic hierarchy process, and then the fuzzy comprehensive evaluation index could be calculated through the establishment of a multi-level fuzzy comprehensive evaluation matrix. At last, the estimation scale of emergency capability of gas pipeline could be obtained.

The cementing quality is directly related to the normal operation of the gas well, therefore, the evaluation of cementing quality is key to the correctly use the gas well as well as to take measures to protect the gas well. In this paper, four first wave amplitudes at the same depth point when using the borehole compensated sonic logger with double transceiver technique to carry out the acoustic amplitude log operation are served as the discriminant factors to evaluate the cementing quality. Taking the engineering actual measured data as the learning samples and using the particle swarm optimization to optimize the parameters of support vector machine, this paper established the intelligent evaluation model for cementing quality based on particle swarm optimization (PSO) and support vector machine (SVM). The model employs the excellent characteristic of SVM which has high speed of solving and could describe nonlinear relation as well as the characteristic of PSO which has global optimization. Through test of engineering samples, the research result showed that this model has fast astringency and high precision, providing a new method and approach for the fast and accurate evaluation of the well cementing quality.

Based on Fisher discriminant theory, the Fisher discriminant analysis model (FDA) was established for predicting the possibility of drilling downhole accidents. Six factors such as WOB、pump pressure、pump flow、running speed、ROPand torque were selected as the discriminant factors of the FDA mode. A series of data from drilling downhole accidents were taken as the training samples, and then some practical engineering datas were used to verify this mode. It was showed that FDA model is one of simple and accurate method in solving the prediction of drilling downhole accidents.

The accurate prediction of gas well productivity is an important task in gas reservoir engineering research. According to the global optimization ability of the genetic algorithm (GA) and the superior regression performance of the support vector machine (SVM), this paper proposed a method based on GA and SVM to improve the prediction accuracy. As the proposed model can reduce the dimensionality of data space and preserve features of gas well productivity, compared with BP neural network model, the proposed GA-SVM model for gas well productivity in practical engineering has higher accuracy and speed, the maximum error is 1.5%. Thus, it provided a new method for the forecast of gas well productivity.

Through investigation of the Dengfeng heating network in the city of Daqing, China, for the 2007–2008 heating season, we found serious problems of excessive heat supply in the primary heating network. Therefore, we propose the application of gas-fired boilers in underperforming heating substations as peak-load heat sources to effectively adapt to the regulation demands of seasonal heat-load fluctuations and reduce the excessive heat supply. First, we calculated the excessive heat supply rates (EHSRs) of five substations using detailed investigative data. We then discussed the feasibility of the proposed scheme providing energy savings from both energetic and exergetic points of view. The results showed that the average EHSR of the five substations between January and March was 20.57% of the gross heat production but consequently reduced to 6.24% with the installation of the gas-fired boilers. Therefore, the combined heating scheme with coal as the basic heat-source and gas-fired boilers as peak-load heat sources is energy-efficient to some extent, although requires the use of natural gas. Meanwhile, the exergy decreased by 10.97%, which indicates that the combined heating scheme effectively reduces the primary energy consumption and pollutant emission of the heating systems.

Combining the machining process simulation on UG NX software and the mathematically analysis, a new solving method for the tooth crest curve equation of spiral bevel gears is proposed in this paper. The steps are as follows:1) Establishing the gear blank cone equation in the original coordinate system; 2) Finding the gear convex and concave profile equations in the new coordinate system; 3) Integrating the original coordinate system and the new one through geometric transformation and then deducing the tooth crest curve equations on both sides. The equations will help calculate the cutter’s position and pose in addendum chamfering process, with the chamfer automation achieved.

The cutter’s position and pose are key elements for chamfering addendum automatically and a new method for calculating the cutter’s position and pose is as follows: 1) Finding the chamfering boundary curves of addendum by offsetting the two top curves (convex and concave) of spiral bevel gear addendum respectively; 2) Dispersing the chamfering boundary curves; 3) Calculating the center position of the tangent circle along the chamfering boundary curves and taking this as the cutter’s center; 4) solving the tilt angle through the center position and the dispersed points on boundary curves. The proposed method lays foundation for chamfering automation.

The universal NC program was inefficient for machining centrifugal pump vanes and a new tool-path generation method along section lines was proposed in this paper. After analyzing curve characteristics of centrifugal pump vanes, the mathematical model for calculating cutting step-lengths and determining the next tool contact parameter ui+1 through step estimating method was put forward. Furthermore, a new iterative algorithm was implemented, along with its terminal condition simplified. The proposed algorithm provided a new idea for developing special NC program of impellers.

In this paper, two modeling methods, the forming method and the generating method, for hypoid gears with two kinds of transmission ratio are discussed by simulating the actual machining process. In the generating modeling method, the tooth profile of the gear is generated by boolean algorithm step by step after creating the models of the gear blank and the cutter and then rotating around their own axis by certain degrees until the cutter is outside the gear blank completely. In contrast with the generating modeling method, the tooth profile is formed by carrying out the boolean algorithm for one time after creating the models of the gear blank and cutter seperately in the forming modeling method. Then using feature instance, all the teeth are created both in the generating modeling method and in the forming modeling method. Using the two modeling methods given in this paper, the modeling process can be shortened and the modeling precision can be improved.

The hydraulic model of the impeller and points of its vane surface given in the cylindrical coordinates, we can not directly use those data to accomplish the 3D solid modeling of the impeller in CAD systems. Based the Access and the UG NX, this paper puts forwards a new method for modeling centrifugal pump impeller vanes and presents the implementing procedure. And the method includes the following steps: 1) defining the data structure of hydraulic models; 2)converting the vane surface data from the cylindrical coordinate system to the cartesian coordinate system; 3)constructing the vane’s working surface and back surface along the axial transversals; 4) accomplishing the impeller’s 3D solid model by UG NX Second Development. The practical application demonstrates that the proposed method can shorten the cycle of impeller modeling and improve the design precision.

Let $T(A,\mathcal{D})$ be a self-affine set generated by an expanding matrix $A=\left[\begin{array}{rr} p & 0\cr -a & q \end{array}\right]$ and a product digit set $\mathcal{D}=\{0,1,\dots,m-1\}\times \{0,1,\dots,n-1\}$. We provide a necessary and sufficient condition for the $T(A,\mathcal{D})$ to be connected, which generalizes the known results., 18 pages

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected. Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively collinear., 18 pages; 18 figures

In \cite{LaLuRa13}, the authors completely classified the topological structure of so called {\it fractal square} $F$ defined by $F=(F+{\mathcal D})/n$, where ${\mathcal{D}}\subsetneq\{0,1,\dots,n-1\}^2, n\ge 2$. In this paper, we further provide simple criteria for the $F$ to be totally disconnected, then we discuss the Lipschitz classification of $F$ in the case $n=3$, which is an attempt to consider non-totally disconnected sets., Comment: 16 pages, 12 figures

To analyze the characteristics of repeated renal biopsy-proven primary focal segmental glomerulosclerosis (PFSGS) in 8 children, and to reveal the relationship between clinical features and pathology, between the two times of renal biopsy pathology, and the indications for repeated renal biopsy.The records of cases who ever experienced renal biopsy in this hospital were reviewed, of whom 8 cases of repeated renal biopsy-proven PFSGS were enrolled. The clinical manifestations, the reason why they had renal biopsy again, the difference in renal pathological findings, between the two biopsies and their therapeutic response. The classification of focal segmental glomerulosclerosis (FSGS) was based on the new criteria suggested by D'Agati in 2004.Of the 8 cases, age of onset ranged from 1 to 12 years, all were diagnosed as nephrotic syndrome (NS), the age of first biopsy ranged from 1.1 to 15.0 years, and the follow-up period was 10 months to 14 years. The reason for repeated biopsy was poor therapeutic response, continuous heavy proteinuria, or the progressive renal dysfunction. Four cases had the both biopsies in this hospital, and the first renal pathology showed minimal change disease (MCD), mesangial proliferation, FSGS CELL type and FSGS GTL type. After the second biopsy, they were additionally treated with immunosuppressive agents or switched to another one, 2 cases with FSGS COLL type presented renal dysfunction or end stage renal disease (ESRD), 1 case who developed the disease at 1.4 years of age, presented renal dysfunction at 10 months follow-up. The remaining 5 cases acquired complete remission.FSGS is a clinicopathological syndrome, NS predominates clinically. It often indicates pathologic transformation when the patients show poor therapeutic response or continuous heavy proteinuria without remission. Mesangial proliferation can convert into FSGS, and the subtype of FSGS can shift. FSGS COLL type and onset at young age may suggest poor prognosis.