Anatomy of the Beginning of the Housing Boom Across U.S. Metropolitan Areas

We provide novel estimates of the location, timing, magnitude, and determinants of the start of the last U.S. housing boom. The last housing cycle cannot be interpreted as a single, national event, as different markets began to boom across a decade-long period, some of them multiple times. A fundamental factor, income of prospective buyers, can account for half of the initial jump in price growth, while expansion of purchases by underrepresented minorities cannot. The start of the boom also was financed conventionally, not by subprime mortgages. The latter's share did rise sharply over time, but only after a multi-year lag.

Recovery problem for a singularly perturbed differential equation with an initial jump

The article investigates the asymptotic behavior of the solution to reconstructing the boundary conditions and the right-hand side for second-order differential equations with a small parameter at the highest derivative, which have an initial jump. Asymptotic estimates of the solution of the reconstruction problem are obtained for singularly perturbed second-order equations with an initial jump. The rules for the restoration of boundary conditions and the right parts of the original and degenerate problems are established. The asymptotic estimates of the solution of the perturbed problem are determined as well as the difference between the solution of the degenerate problem and the solution of the perturbed problem. A theorem on the existence, uniqueness, and representation of a solution to the reconstruction problem from the position of singularly perturbed equations is proved. The results obtained open up possibilities for the further development of the theory of singularly perturbed boundary value problems for ordinary differential equations.

Uniform Approximation to the Solution of a Singularly Perturbed Boundary Value Problem with an Initial Jump

In this study, a third-order linear integro-differential equation with a small parameter at two higher derivatives was considered. An asymptotic expansion of the solution to the boundary value problem for the considered equation is constructed by considering the phenomenon of an initial jump of the second degree zeroth order on the left end of a given segment. The asymptotics of the solution has been sought in the form of a sum of the regular part and the part of the boundary layer. The terms of the regular part are defined as solutions of integro-differential boundary value problems, in which the equations and boundary conditions contain additional terms, called the initial jumps of the integral terms and solutions. Boundary layer terms are defined as solutions of third-order differential equations with initial conditions. A theorem on the existence, uniqueness, and asymptotic representation of a solution is presented along with an asymptotic estimate of the remainder term of the asymptotics. The purpose of this study is to construct a uniform asymptotic approximation to the solution to the original boundary value problem over the entire considered segment.

Monopoly behavior of China’s manufacturing enterprises

Purpose With the increase of state capital, corporate total factor productivity (TFP) has a tendency to jump up at first and then slowly decrease. Generally, no significant “productivity paradox” can be observed in China’s manufacturing industry. With the increase of export density, corporate TFP also shows a trend of initial jump growth and subsequent slow decline. This paper aims to discuss these issues. Design/methodology/approach Using the 1996–2013 China Industrial Enterprise Database, this paper studies the monopolistic behavior of Chinese manufacturing enterprises through the measurement of TFP and corporate monopoly power. Findings Results show that China’s manufacturing monopoly enterprises are generally innovation-oriented rather than rent-seeking. However, there are certain differences between diversified types of monopoly enterprises: the ones with state capital are more inclined to innovate than those without, whereas the ones with export delivery value are more inclined to seek rent than those without. Originality/value Therefore, the government should implement differentiated policies for diversified types of monopoly enterprises, and do so in a targeted manner fully reflecting the containment of rent-seeking and the encouragement of innovation.

ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION

In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

Dispersive shock waves in colloids with temperature dependent compressibility

The formation of a dispersive shock wave in a colloidal medium, due to an initial jump in the light intensity, is studied. The compressibility of the colloidal particles is modeled using a series in the particle density, or packing fraction, where the virial coefficients depend on the particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results for the second virial coefficient show that it is temperature dependent and that the particle interactions can be either repulsive or attractive. These effects are modeled using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump is resolved via a dispersive shock wave which forms before the onset of modulational instability. A semi-analytical solution is developed for the one-dimensional line bore case which predicts the amplitude of the solitary waves which form in the dispersive shock wave. The solitary wave amplitude versus jump height diagrams can exhibit three different kinds of behaviors. A unique solution, an S-shaped solution curve and multiple solution branches where the upper branch has separated from the lower branches. A bifurcation from the low to the high power branch can occur for many parameter choices as the amplitude of the initial jump increases. The effect of temperature on the evolution of the bore, the amplitude of the solitary waves and the bifurcation patterns are all discussed and the semi-analytical solutions are found to be very accurate.

Asymptotic Estimates of the Solution of a Restoration Problem with an Initial Jump

The asymptotic behavior of the solution of the singularly perturbed boundary value problemLεy=htλ,Liy+σiλ=ai,i=1,n+1̅is examined. The derivations prove that a unique pair(ỹt,λ̃ε,ε,λ̃ε)exists, in which componentsy(t,λ̃ε,ε)andλ̃(ε)satisfy the equationLεy=h(t)λand boundary value conditionsLiy+σiλ=ai,i=1,n+1̅. The issues of limit transfer of the perturbed problem solution to the unperturbed problem solution as a small parameter approaches zero and the existence of the initial jump phenomenon are studied. This research is conducted in two stages. In the first stage, the Cauchy function and boundary functions are introduced. Then, on the basis of the introduced Cauchy function and boundary functions, the solution of the restoration problemLεy=htλ,Liy+σiλ=ai,i=1,n+1̅is obtained from the position of the singularly perturbed problem with the initial jump. Through this process, the formula of the initial jump and the asymptotic estimates of the solution of the considered boundary value problem are identified.

Effects of Fatigue on Kinetic and Kinematic Variables During a 60-Second Repeated Jumps Test

Purpose:The aim of this study was to investigate the effects of a maximal repeated-jumps task on force production, muscle activation and kinematics, and to determine if changes in performance were dependent on gender.Methods:Eleven male and nine female athletes performed continuous countermovement jumps for 60 s on a force platform while muscle activation was assessed using surface electromyography. Performances were videotaped and digitized (60 Hz). Data were averaged across three jumps in 10-s intervals from the initial jump to the final 10 s of the test.Results:No interaction between time and gender was evident for any variable; therefore, all results represent data collapsed across gender. Preactivation magnitude decreased across time periods for anterior tibialis (AT, P < .001), gastrocnemius (GAS, P < .001) and biceps femoris (BF, P = .03), but not for vastus lateralis (VL, P = .16). Muscle activation during ground contact did not change across time for BF; however, VL, G, and AT showed significant reductions (all P < .001). Peak force was reduced at 40 s compared with the initial jumps, and continued to be reduced at 50 and 60 s (all P < .05). The time from peak force to takeoff was greater at 50 and 60 s compared with the initial jumps (P < .05). Both knee fexion and ankle dorsifexion were reduced across time (both P < .001), whereas no change in relative hip angle was evident (P = .10). Absolute angle of the trunk increased with time (P < .001), whereas the absolute angle of the shank decreased (P < .001).Conclusions:In response to the fatiguing task, subjects reduced muscle activation and force production and altered jumping technique; however, these changes were not dependent on gender.