Chromatographic experiments were performed on C18 column(4.6 mm×250 mm,5μm),the mobile phase was methanol and water(3070); the detection wavelength was 236 nm,column temperature was 30 ℃,the flow rate was 1.0 ml/min.

固定相为汉邦C18色谱柱(4.6 mm×250 mm,5μm),流动相为甲醇-水(30:70),检测波长为236 nm,柱温:30℃,流速:1.0 m l/m in。

Chromatographic colum was KromosilTM ODS-2 column(150 mm×4.6 mmi.d.,5 μm), mobile phase was acetonitrile-0.4%phosphonic acid(13∶87) with flow rate of 1.0 mL/min, detection wave length was 327 nm.

METHODS A primary analysis was carried out on symetry shield C18 column(250 mm×4.6 mm,5 μm),with acetonitrile and water as mobil phase(griadient flow) and flow rate of 1.0 ml·min-1.ELSD and UVD were used as detectors.

The operating conditions by HPLC were C18 column(250 mm× 4.6 mm), v(methanol)∶v(water)=70:30 as mobile phase,1 mL/min as flow speed and wavelength 220 nm.

After giving a suitable model for the cutting strips problem, we present a branch-and-price algorithm for it by combining the column generation technique and the branch-and-bound method with LP relaxations.

Some theoretical issues and implementation details about the algorithm are discussed, including the solution of the pricing subproblem, the quality of LP relaxations, the branching scheme as well as the column management.

Let U(R,S) denote the class of all (0,1)-m × n matrices having row sum vector R and column sum vector S.

Enumeration of (0,1)-matrices with constant row and column sums

Let fs,t(m,n) be the number of (0,1) - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones (sm = nt).

Single storied industrial buildings composed of steel trusses and reinforced-concrete columns are very common. As the upper joints are hinged, the stresses in the columns are not influenced by the elastic properties of the trusses; while the upper joints are rigid, methods of analysis are usually based on the assumption that the moment of inertia of a steel truss may be taken as equivalent to that of a beam. In this paper, the author making use of the principle of least work reviews the equations...

Single storied industrial buildings composed of steel trusses and reinforced-concrete columns are very common. As the upper joints are hinged, the stresses in the columns are not influenced by the elastic properties of the trusses; while the upper joints are rigid, methods of analysis are usually based on the assumption that the moment of inertia of a steel truss may be taken as equivalent to that of a beam. In this paper, the author making use of the principle of least work reviews the equations for calculating the angle-changes at the ends of a truss, and then illustrates their applications with two practical examples: one with flat roof and the other with gabled-roof. They are solved respectively by the method of slopedeflection for the cases of no-sidesway, sidesway-correction and sidesway included by solving the elastic equations of unit deformation. The results are compared with those obtained with usual assumptions.

This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the...

This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the sum of modified stiffness of all the bar-ends at a joint as the auxiliary frame constant. The basic frame constants at the left of right ends of all the bars are computed by the consecutive applications of a single formula in a chain manner. The auxiliary frame constant at any joint where it is needed is computed from the basic frame constants at the two ends of any bar connected to the joint, so that its value may be easily checked by computing it from two or more bars connected to the same joint.Although the principle of this method was developed by Dr. Klouěek and Prof. Meng, the formulas presented in this paper for computing the basic and auxiliary frame constants, besides being believed to be original and by no means the mere amplification of those presented by the two predecessors, are of much improved form and more convenient to apply.By the author's formula, the basic frame constants in closed frames of comparatively simple form may be computed in a straight-forward manner without much difficulties, and this is not the case with any other similar methods except Dr. Klouěek's.The case of sidesway is treated as usual by balancing the shears at the tops of all the columns, but special formulas are deduced for comput- ing those column shears directly from joint rotations and sidesway angle without pre-computing the moments at the two ends of all the columns.In the method of propagating unbalanced moments proposed by Mr. Koo I-Ying and improved by the author, the unbalanced moments at all the bar-ends of each joint are first propagated to the bar-ends of all the other joints to obtain the total unbalanced moments at all the bar-ends, and then are distributed at each joint only once to arrive at the balanced moments at all the bar-ends of that joint. Thus the principle of propagating joint rotations with indirect computation of the bar-end moments is ingeneously applied to propagate unbalanced moments with direct computation of the bar-end moments, and, at the same time, without the inconvenient use of two different moment distribution factors as necessary in all the onecycle methods of moment distribution. The basic frame constant employed in this method is the same as that in the method of propagating joint rotations, so that its nearest approximate value at any bar end may be computed at once by the formula deduced by the author. Evidently, this method combines all the main advantages of the methods proposed by Profs.T. Y. Lin and Meng Chao-Li and Dr. Klouěek, and is undoubtedly the most superior one-cycle method of moment distribution yet proposed as far as the author knows.Typical numerical examples are worked out in details to illustrate the applications of the two methods.

The so-called "truss rigid frames" are those rigid frames with trusses as their horizontal beams, of which the two ends are rigidly connected to columns. Within the author's knowledge, all the methods available at present for analyzing such rigid frames are based on Certain special assumptions such as (1) that the positions of the points of contra-flexure in all the columns are previously known; (2) that the end rotations of a truss may be reprensented by that of its assumed line of axis as in the...

The so-called "truss rigid frames" are those rigid frames with trusses as their horizontal beams, of which the two ends are rigidly connected to columns. Within the author's knowledge, all the methods available at present for analyzing such rigid frames are based on Certain special assumptions such as (1) that the positions of the points of contra-flexure in all the columns are previously known; (2) that the end rotations of a truss may be reprensented by that of its assumed line of axis as in the case of an ordinary beam; or (3) that the end verticals of trusses may be given certain prescribed deformations. Of course, the adoption of any of such assumptions leads to only approximate results inconsistent with the actual deformations of such rigid frames under any loading. Heretofore, the author did not know any correct method for analyzing such rigid frames. In this paper, the author presents two principles of the correct analysis of truss rigid frames. The first principle is that of "moment action on column" for computing the angle change constants of columns, and the second principle is that of "effect of span-change in truss" for computing the angle and span change constants of trusses.As, for computing the angle change constants of a truss, the dummy unit moment is a couple applied to its end verticals, so, for computing the angle change constants of a column, the dummy unit moment must also be a couple applied to the section of column rigidly connected to the end of a truss, in order to effect a consistent deformation at the joint of the two. This is the first principle.A truss just like a curved or gabled beam of which the effect of span-change can not be neglected, so truss rigid frames belong to the same category of what may be called "span-change" rigid frames such as rigid frames with curved or gabled beams. Therefore the span-change constants of trusses should be included besides their angle-change constants for analyzing truss rigid frames. This is the second principle.With the constants of columns and trusses are all computed in accordance with respectively the first and second principles mentioned above, truss rigid frames may be analyzed by any method including the effect of span-change as in the case of rigid frames with curved or gabled beams, and the results thus obtained will be exactly the same as by the method of least work or deflections without any special assumptions.In this paper, after the two principles are described and the formulas for computing the constants of columns and trusses are derived, the correctness of the two principles are then proved by the methods of least work, deflections and slope-deflection. A two-span truss rigid frame is analyzed under the following three conditions:Ⅰ. Applying both of the two principles to obtain the correct results.Ⅱ. Applying only the first principle to show the discrepancies of neglecting the effect of span-change in trusses as born out by comparing the results of Ⅱ with Ⅰ.Ⅲ. Applying neither of the two principles, and the truss rigid frames being analyzed by the special assumption (2) mentioned above with the line of axis at the bottom chord of truss, in order to show the discrepancies of neglecting the moment action on column as born out by comparing the results of Ⅲ with Ⅱ. For the sake of brevity, only the results are given in Tables 1 to 5 without computations in details.Although the discrepancies of neglecting the moment acticn on column are only slight as shown by comparing the results of Ⅲ with Ⅱ in Tables 2, 4 and 5, there is no reason why special assumptions should not be replaced by the correct principle of moment action on column to obtain correct results. As shown by comparing the results of Ⅱ with Ⅰ in Tables 2, 4 and 5, the discrepancies by neglecting the span change in trusses are generally considerable and, in certain particular part, as large as 3000%. Therefore, for the safe and economical design of truss rigid frames, the effect of span-change in trusses should not be neglected in their analysis.Finally, for analyzing co