Optimal Endogenous Growth with Exhaustible Resources

We study optimal research and extraction policies in an endogenous growth model in which both production and research require an exhaustible resource. It is shown that optimal growth is not sustainable if the accumulation of knowledge depends on the resource as an input, or if the returns to scale in research are decreasing. The model is stated as an infinite-horizon optimal control problem with an integral constraint on the control variables. We consider the main mathematical aspects of the problem, establish an existence theorem and derive an appropriate version of the Pontryagin maximum principle. A complete characterization of the optimal transitional dynamics is given

Екологічні наслідки виробничої діяльності в Україні: фрагмент історії (1970-1980)

У роботі показано, як жорстка орієнтація на виробничі пріоритети внесла разючої змiни в навколишнє середовище, поглибила екологічну кризу в суспільстві. Домiнуюча технократична парадигма науково-технічної і виробничої діяльності витиснула у соцiальній свiдомості те, що навколишнiй свiт iснує не лише для задоволення матерiальних потреб

Petrophysical Characterization of Shales Utilizing Laboratory and Field NMR

Over the years, service companies designed numerous tools for field NMR measurements. Amongst them are CMR-Plus with Schlumberger, MRIL-Prime with Halliburton and MREX with Baker Hughes. NMR logs found success in application to conventional fields, but their application to shales remains a challenge. An impediment to evaluation is due to confinement of fluids to nanometer pores, organic and non-organic porosity, paramagnetic impurities, as well as limitations of the current logging tools. We evaluated applicability of two of these tools in shales with guidance from the results of the laboratory NMR experiments. Tuscaloosa Marine Shale, TMS, was logged with a CMR-Plus at 200 fph and 350 fph and Woodford Shale with an MRIL-Prime tool. We conducted 1D as well as 2D laboratory NMR experiments on both shales. Tests were performed at the same echo spacing (TE) as the field logging tools, as well as at TE = 0.114 ms. Measurements were obtained on the as received, cleaned, brine imbibed and pressure saturated (5000 psi), dodecane imbibed and pressure saturated (5000 psi) sample states. NMR measurements in Woodford shale indicate that storage capacity is underestimated by over 55% with echo spacing ranging from 0.6 ms to 0.114 ms. Service companies attempt to compensate for this by applying extrapolation algorithms to TE = 0 ms. However, we show that extrapolation practices should be conducted with caution. In order to tie NMR results between laboratory and field measurements data should be acquired at the same TE values. Additionally, T2 cutoffs, which are often utilized for the purposes of distinguishing movable and residual fluids, are non-unique and are a strong function of echo spacing. Assuming a T2 cutoff of 0.8 ms, we show on the TMS samples that by varying echo spacing from 0.4 ms to 0.114 ms, movable fluid content was overestimated by 45%. In TMS, mercury injection and NMR results from imbibition and pressure saturation experiments reveal that the pore network is inaccessible to dodecane due to strong affinity for water and high capillary entry pressure. Vertical fractures are apparent in the NGI image log in addition to microfractures observed in the SEM images. Based on the laboratory measurements, it appears that the TMS matrix cannot store hydrocarbons. Unlike other shale plays, hydrocarbons in TMS are likely stored and produced from the microfractures, rather than from organic or inorganic pore system. Fluids, confined to the nanometer size pores, were investigated with NMR in the early maturity window of Woodford samples. 1D T2 measurements were not effective in distinguishing brine from low viscosity hydrocarbon (dodecane). T1-T2 signatures of Woodford samples spontaneously imbibed and pressure saturated at 5000 psi with brine and dodecane, as well as NMR response from the non-movable fluids, were obtained with a 2 MHz Oxford-Maran GeoSpec2 spectrometer at TE = 0.114 ms. Samples showed increasing T1/T2 ratio to dodecane following pressurized saturation: dodecane imbibition T1/T2 ≥ 5, dodecane saturation T1/T2 ≥ 10. Small, non-wetting pores are accessed through pressurized saturation, on the order of 4 nm when pressurized with dodecane at 5000 psi. Implications of these finding is such that low viscosity hydrocarbons confined to nanometer size pores experience increasing correlation times or decreasing rotational mobility. Additionally, non-movable hydrocarbons, which remained in the Woodford samples following pressurized cleaning with solvents, showed T1/T2 ≥ 30. Therefore, in nanometer size pores, T1-T2 signatures of low viscosity hydrocarbons and viscous hydrocarbons are likely to overlap

Экологические последствия производственной деятельности в Украине: фрагмент истории (1970-1980-ые годы)

У роботі показано, як жорстка орієнтація на виробничі пріоритети внесла разючої змiни в навколишнє середовище, поглибила екологічну кризу в суспільстві. Домiнуюча технократична парадигма науково-технічної і виробничої діяльності витиснула у соцiальній свiдомості те, що навколишнiй свiт iснує не лише для задоволення матерiальних потреб.It is shown as a rigid focus on manufacturing priorities brought amazing changes in the environment, ecological crisis deepened in society. Dominant technocratic paradigm of scientific, technical and production activities in social superseded svidomosti that the surrounding world exists not only to meet the needs of material.В работе показано, как жесткая ориентация на производственные приоритеты внесла поразительной изменения в окружающую среду, углубила экологический кризис в обществе. Доминирующей технократическая парадигма научно-технической и производственной деятельности вытеснила сознание, что окружающий мир существует не только для удовлетворения материальных потребностей

Nonstationary flow for the Navier-Stokes equations in a cylindrical pipe

In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier-Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force and initial velocity of the flow, but with no smallness restrictions on the inflow, initial velocity neither force, we prove existence of solutions in $W^{2,1}_2.

Boundary Conditions for Singular Perturbations of Self-Adjoint Operators

Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let \tau:D(A)\to\X, X a Banach space, be a surjective linear map such that \|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range} (\tau')\cap\H' =\{0\}, we define a family $A^\tau_\Theta$ of self-adjoint operators which are extensions of the symmetric operator $A_{|\{\tau=0\}.}$. Any $\phi$ in the operator domain $D(A^\tau_\Theta)$ is characterized by a sort of boundary conditions on its univocally defined regular component \phireg, which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These boundary conditions are written in terms of the map $\tau$, playing the role of a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension parameter $\Theta$ being a self-adjoint operator from X' to X. The self-adjoint extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in which $A\phi=T*\phi$ is a convolution operator on LD, T a distribution with compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and Applications, vol. 13

Global well-posedness for the KP-I equation on the background of a non localized solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in $x$ and $y$ periodic or conversely)

A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity

In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity $k$ are allowed to depend both on the order parameter $chi$ and on the absolute temperature $theta$ of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions

Development of the solar plant for heat supplying of the educational laboratory campus

The paper deals with solar plant, that provides heat water supplying of the Ural Federal University Heat, gas supplying and ventilation department educational laboratory campus. The paper presents the installation scheme of solar plant, it's operating principle and events that related with plant operating and working.Рассматривается теплогенерирующая установка с использованием плоских солнечных коллекторов, обеспечивающая горячее водоснабжение учебно-лабораторного корпуса кафедры ТГиВ УрФУ за счет возобновляемой (солнечной) энергии. Представлена схема, характеристики, принцип работы и мероприятия, проводимые и планируемые по обслуживанию установки