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The paper shows how the describing function technique can be employed in a search for periodic solutions to large systems of nonlinear differential equations that describe chemical reaction networks of a type encountered in biological contexts. The equations studied describe a reaction scheme in which the first reaction is inhibited by the product of the last reaction. The differential equations take the form dS 1 ⧸dt = K⧸( 1 + α(S n ) ρ ) and dS j ⧸dt = g j− 1 S j− 1 −b j S j , j = 2, 3,⋯n . The parameter ϱ is a positive integer and represents the number of molecules of inhibitor required to block the S 1 to S 2 reaction. The equations can be interpreted as a simple model of inhibition of transcription, or they can be interpreted as an inhibited enzyme reaction system in which initial substrate concentration and enzyme concentrations are held constant. The system of simultaneous equations is reduced to a single equation in S n : (p + b 1 )(p + b 2 )⋯(p + b n )S n = d 1 /( 1 + d 2 S ρ n ) . Here p is the differentiation operator and d 1 and d 2 are positive constants expressible in terms of α, g j 's, and K . The transfer function block diagram equivalent to this equation is established, and is seen to have closed feedback loop form and to contain a linear block and a nonlinear block. The nonlinear block is replaced by the describing function which is related to the Fourier series of the nonlinear block's output. A study of the system containing the describing function is then developed. It is shown that if ϱ =1, then the describing function analysis indicates, for arbitrary n , that stable limit cycles will not appear if K , α, g j , and b j are positive. Since these constants represents the products of reaction rate constants and concentrations, this requirement is automatically met. The nonexistence of stable limit cycles for ρ =1 holds for all values of n ; it is also shown that for n ⩽4 unstable limit cycles are also necessarily absent. The extension of the method for larger values of ρ is outlined. Since the 1 (1 + z ρ ) nonlinearity frequently appears in biological problems, the describing function will be useful in several areas of research.

An additional analysis of our low-temperature and high magnetic field measurements of the3He melting curve is presented, based on the assumption that the highest field (63.6 kG) theoretical melting curve is correct rather than the lowest field curve as assumed in the original paper. Between31.8 and63.6 kG there is reasonable agreement between experiment and theory, although a discrepancy remains at low fields that we assume is to be attributed to inaccuracies in the reduction of γ-ray anisotropies to temperatures. It is also shown that the measurements are not sufficiently precise to observe the effect seen in the(∂P/∂T) V,H measurements on solid3He by Kirk and Adams.

Water table recession in an irrigation project in southern Alberta was compared with moisture translocation in covered lysimeters during two winters. Upward translocation to the surface 60 cm during one winter amounted to 1 to 2 cm of water in dry soils having a grass cover, and 2 to 2.3 cm in moist soils with no vegetation. Observations between growing season and freeze-up indicated that a considerable amount of water may drain downward. The upper 30 cm of soil generally is not influenced by upward translocation if the soil is dry before freeze-up.

This paper is an extension of, and complementary to, an earlier paper by Wheatley, Vilches, and Abel. Some important fundamental questions which lead to degradation in the performance of a dilution refrigerator are considered: namely, convection on the dilute side and superfluid on the concentrated side. Experimental results are presented for a film suppressing still used in conjunction with a continuous-heat exchanger (several designs are considered) and a variable number (0–6) of step-heat exchangers of a copper-foil type with a high surface-area-to-viscous-impedance ratio. The first quantitative measurements of viscous heating on the dilute side are presented as well as measurements of thermal resistance on the dilute and concentrated side. Finally, the properties of the refrigerator under external heat load are considered.

The thermal expansion of 15 alkali halides has been investigated from 70 to 570 K. The single‐crystal specimens of LiF, LiCl, LiBr, NaF, NaCl, NaBr, NaI, KF, KCl, KBr, KI, RbI, CsCl, CsBr, and CsI are examined using a high‐precision differential dilatometer in conjunction with an electronic micrometer. The results are compared with those available in the literature and are found to be in reasonable agreement. The Gruneisen parameter γ has been calculated using the present thermal expansion data. For a given cation group, the value of γ is very close, but increase in the cation size decreases γ slightly. The indications are that in the temperature range under investigation γ increases very slowly with temperature.

An analytic method is presented which can be used to determine if the following system of nonlinear differential equations has periodic solutions x1 = h(xn)-b1x1 xj = gj-1xj-1-bjxj j = 2, ... n A systematic dual input describing function procedure is given for constructing a function of the reaction constants R, where if R greater than 1 a periodic solution exists and if R smaller than 1 there is no periodic solution. The form of R constructed generalizes immediately to an arbitrarily large dimension. The method generalizes to cover systems displaying hysteresis kinetics, systems subject to chemical noise, and systems containing delay components. The method has been applied to a well known biochemical problem where h(xn)-k/(1 + alphaxnrho). For rho = 1, for all n, there are no stable limit cycles such that xj(t) greater than O, t larger than or equal to O. For rho = 2,n larger than or equal to 8 it is possible to construct a parameter set such that stable oscillations appear.

A 1971 poll at Drexel University showed that 89% of the female student body polled favored the hiring of a gynecologist by the University health center. 85% felt the health center should prescribe contraceptives. A subsequent poll in 1972 showed that 49% had had gynecological problems while at Drexel and 65% had received contraceptives during that period. It is recommended that contraceptives be provided through the health service on a fee-for-service basis because: 1)students are significantly in favor of it; 2)67% would use the service; 3)the service could be less expensive than the private physicians and more personal than the Planned Parenthood clinic now used by the students; and 4) the psychically damaging effects of unwanted pregnancy and abortion could be avoided. Gynecological services should be provided free of extra charge by the health center.

Samples of grade A Monel snd grade A nickel were subjected statically in a single reactor to an undiluted atmosphere of gaseous fluorine at pressures up to one atmosphere absolute and temperatures up to 1500 deg F. The grade A Monel was conservatively estimated to have consumed at least 40 times as much fluorine as grade A nickel during the entire period of the investigation. Samples of fused alpha Al/sub 2/O/sub 3/, alpha -Al/sub 2/O/sub 3/- MgO spinel, and alpha -Al/sub 2/O/sub 3/-NiO--nickel cermet were exposed to undiluted fluorine at one atinosphere absolute pressure at temperatures of 1340 and 1500 deg F. Results indicated that the alpha -Al/sub 2/O/sub 3/ is as good as the Ni in the region of 1300 deg F. Grade A nickel samples coated with nickel fluoride filins of 37,000 and 74,000 A, respectively, were exposed to an absolute pressure of gaseous UF/sub 6/ of 12 cm of Hg at temperatures of 1000 and 1800 deg F. (W.L.H.)

By use of a modified thermobalance and reactor as the primary experimental tool for sample preparation and evaluation, a process has been developed by which parent uranium feed materials of a widely variable reactivity and composition may be converted to a uniformly reactive uranium dioxide.

Two thermobalances have been constructed which make use of an improved reactor design for the study of gas-solid reactions as they apply to the conversion of uranium oxide materiels to uranium tetrafluoride. Since temperature has been recognized as one of the most important rate-governing factors for both of the reactions involved in this transformation, the reactor design provides for maintaining the sample temperature constant to +- 1.0 deg C. at any selected temperature over the range 100 to 600 deg C. Rate-controlling variables such as reaction temperatures, gas flow rates, preheating time and bed depth have been studied in order to establish the ranges over which small variations in these factors can be ignored. (auth)

The Hamilton National Associates, Inc., of Chattanooga, is a holding company for seventeen banks in northern Georgia and eastern Tennessee. Fourteen of these banks have assets ranging from $400,000 to $2,500,000 each; one in Johnson City has $7,000,000; another in Knoxville, $40,000,000; and the head office in Chattanooga over $70,000,000. The Chattanooga bank has four local branches, thus giving the system a total of twenty-one banking offices. The consolidated report for December 31, 1941, indicates resources of over $139,000,000 for the group as a whole. The operations of the Hamilton Group provide an unusual opportunity to study the methods and results of group banking. The system was among the earliest to be organized. It weathered the severe financial storms of the depression years. There is no other multiple-bank system in the area served. In some towns there is active local competition, whereas in others the Group bank is the only financial institution. The development has embraced not only unit and group banking but also branch banking, and thus it reflects the trend toward banking concentration in other parts of the United States.2 Lastly, the President of the Hamilton National Associates, Thomas R. Preston, has been an influential figure in political, industrial, and financial circles, having served as President of both the Tennessee and the American Bankers Associa

Mutual savings banks in Connecticut, like those in Massachusetts and New York State, have been in the life insurance business for many years. They have been direct writers exclusively because the law authorizing them to sell life insurance provides that they may not employ solicitors or house-to-house premium collectors. The legislatures of the three states extended this unique franchise so that an economical system of direct-purchase life insurance would be available to the public. There is also a statutory limitation placed on the amount of savings bank life insurance that may be issued on one life under ordinary forms of policies. Here the state laws differ. In Massachusetts, the legal limit is $1,000 multiplied by the number of insurance writing banks, and with forty-three such banks in the system at the present time, the maximum face value of coverage is $43,000. The New York limit is $10,000 on life and endowment forms of policies plus $20,000 de

Excerpt To the editor: In "Adolescent Crisis" (Ann Intern Med79:435-440, 1973) Miller points up the need to develop physicians who are sensitive to the problems of adolescents. It seems to me, as I...