Function Of Several Independent Variables Research Articles

Statistical analysis on length of stay in hospital

The rising financial problems of healthcare institutions make studies of resource distribution more and more important and valuable. Among these studies, identification of length of stay of hospital patients (LOS) has attracted many scientists recently since it contributes to better knowledge of hospital costs and helps these institutions control the costs. This paper is devoted to study the length of stay of inpatients in hospital. Although predicting the length of stay is difficul, it is actually useful and benificial if some key factors that have influence on patient length of stay could be determined. This paper will be the basis for a running example that illustrates alternative models of the length of stay of hospital pentients. A total of 1189 episodes, which contains patient records, were analyzed by using some parametric and nonparametric statistical methods. In this study, several factors are first considered and investigated, including date of admission, medical admission unit, dianogsis result, international classification of diseases (icd), age, province, profession, recovery status when discharged, ethnic, and etc. Multiple regression analysis was also carried out for modeling length of stay as a function of several independent variables. Since the number of inpatient hospital stays is concerned, the family of Poisson distributions is used in this study. This approach is also supported by the corresponding histogram. Furthermore, univariate analyses showed that age, province, profession, admission quarter, recovery status when discharged, and diseases significantly influence on LOS. Finally, multivariate analysis of multiple regression model emphasized that type of disease, admission quarter, age group, and profession are the key factors that influence the LOS. These results may have some economic and clinical implications for not only patients but also hospitals.

Optimized tabu search estimation of wear characteristics and cutting forces in compact core drilling of basalt rock using PCD tool inserts

Monitoring of cutting tool wear is crucial in machining operations where planning for longer tool life would result in economical savings. While deterministic and stochastic methods were sought for identifying optimal cutting conditions, efficiency and/or accuracy of the generated model fits were found to suffer when dealing with large number of variables. In this work, we present a novel method for tool wear optimization that combines tabu search algorithm with regression analysis (dubbed TS-REG). First, this method is validated against literature-reported model equation fitting of several modeling studies of turning, end milling, and drilling processes. Corroboration of TS-REG is established having found that it outperforms other techniques such as REG, artificial neural networks (ANN), and genetic algorithm (GA). Then, TS-REG is utilized to estimate tool wear and cutting forces for efficient core drilling of basalt rock, a hard and abrasive component of the Martian surface. For cutting data, this work utilizes previously reported tool wear and force data by Hamade and coworkers of polycrystalline diamond (PCD) compact core drilling experiments. The cutting data is comprised of dependent variables of tool wear (flank wear and cutting edge radius wear) and forces (thrust force and torque)as function of several independent variables (process parameters) namely rake angle, spindle speed, tool feed, rock specimen’s ultimate compressive strength, UCS , specimen rock type, and drilled depth. These independent variables and their combinations resulted in fit equations with total number of 117 different variables. As compared with conventional REG and ANN fit estimates of the same data, TS-REG was found to yield the best statistical estimates of tool wear and cutting forces model equations where all dependent parameters were included in the model. Statistical metrics used for assessment of the fitted models were p-value, R-squared, and mean absolute percentage error.

A novel approach for operational optimization of multi-stage refrigeration cycles in gas refineries

The efficient use of energy in refrigeration cycles of gas liquefaction plants is a contemporary topic of interest. The previous optimization studies on refrigeration cycles have not considered the components' operational limitations. By considering the fact that in operating plants, all constraints must be thoroughly taken into account, this paper presents a novel approach for operational optimization of in-use refrigeration cycles which takes into account the operational limitations of the components as well as the interaction between the refrigeration cycle and the core process. This novel approach exploits a combination of thermodynamic principles and pinch technology to express the multi-stage refrigeration cycles' power consumption as a function of several independent variables. To examine the applicability of the proposed approach, it is used to optimize a three-stage refrigeration cycle in a propane liquefaction plant. About 15.4% reduction in the specific power consumption is achieved.

Study regarding the springback of metal sheet parts after bending

Plastic deformation of materials is accompanied by elastic deformation. After the bending process, the elastic deformation disappears and the part is changing its dimensions comparing with those of the tool. The change of bent part’s dimensions due to the elastic properties of material is called elastic springback . It influences the precision of bent parts, especially the bending angle, and this is why its value should be known in order to take the necessary measures in order to reduce or even annihilate its effects. Its value can be determined with analytical relations, from various nomograms or with experimental relations. Because the analytical relations offer results far from reality, this paper proposes a multivariable relation of springback (dependent variable) as a function of several independent variables obtained on the basis of experimental results, in real working conditions and using the method of regression functions. This method is based on simultaneous variation of considered variables, using a limited number of values in the experimentation domain. A split experimental program was used. The obtained relation is true for any combination of values for considered variables, but, from their variation domains, it can be obtained separately the effects of independent variables on dependent variables.

Inequalities for Partial Derivatives and their Applications

AbstractWe present various weighted integral inequalities for partial derivatives acting on products and compositions of functions that are applied in order to establish some new Opial-type inequalities involving functions of several independent variables. We also demonstrate the usefulness of our results in the field of partial differential equations.

Fast Jacobian Mie Library for Terrestrial Hydrometeors

This paper presents an approach for the fast accurate computation of several useful Mie-based parameters for homogeneous, spherical, liquid water, and ice hydrometeor distributions over a wide range of frequencies, mean hydrometeor diameters, and physical temperatures as occur in the terrestrial atmosphere. The absorption coefficient, scattering coefficient, backscattering coefficient, and phase asymmetry parameters are cast into functions of three independent variables: frequency, temperature, and mean diameter. An exponential drop size distribution with a constant fractional volume of is used to model polydispersed hydrometeors. The ranges used for frequency, temperature, and mean diameter are [1, 1000] GHz, , and [0.002, 20] mm, respectively. The functions are then sampled on a logarithmic grid. Trivariate cubic spline interpolation using nonuniform basis splines (B-splines) is then used to efficiently represent these 3-D functions in a compact library. By using this method, four important criteria are achieved: 1) fast random computability of any of these parameters given the values of frequency, temperature, and mean diameter; 2) minimal memory usage by storage of only B-spline coefficients; 3) representation of parameters using well-behaved functional forms amenable to analytical differentiation for the evaluation of Jacobians, or alternatively, for higher accuracy, B-spline coefficients calculated using true Jacobian values can be used; and 4) negligibly small and bounded error over the entire domain of the library. These procedures result in considerable acceleration of microwave radiative transfer simulations across a broad frequency spectrum, as demonstrated in calculations for both scattering and nonscattering atmospheres. The methods discussed can also be applied to other geophysical problems requiring rapid calculation of series-based functions of several independent variables, where the function evaluation is a time-consuming process, and maximum error bounds are critical.

Multivariable analysis of energy decay in coupled volume rooms: How can we objectively describe what we perceive in coupled volume performance spaces

The behavior of coupled volumes in room acoustics is commonly characterized by multiple slopes observed in sound energy decay curves, as measured (or modeled) using an omnidirectional receiver. This characterization is often limiting and can not adequately explain the change in character of sound energy decay with time that we perceive as listeners in music performance spaces that employ coupled volumes. By investigating energy decay as a function of several independent variables, including time, frequency, and direction of energy arrival, we seek to forge new objective measures that relate to what a listener actually hears in a coupled volume concert hall. We will discuss relevant geometry and materials of several coupled volume performance spaces designed by Artec Consultants Inc, describe subjective phenomena we have observed in these halls, and present results of our ongoing investigation of new objective metrics geared to better characterize coupled volume music performance spaces.

Mitochondrial DNA Amplification Success Rate as a Function of Hair Morphology

This study examines the amplification success rate of mitochondrial DNA from human head hair with respect to their potential for forensic application. Mitochondrial DNA was isolated using a Chelex-based extraction method and amplified using the LINEAR ARRAY duplex PCR system. The particular focus of this study was to characterize the morphological features of human head hair in order to further the understanding of the factors that influence amplification success rate in hair tissue using the LINEAR ARRAY duplex PCR system. 2554 head hairs from 132 individuals representing four population groups were amplified. The hair samples were characterized as follows: 1251 were identified microscopically as telogen hairs and 1303 were classified as hairs without roots (removed before extraction). Amplification success was assessed as a function of several independent variables: morphological characteristics; telogen root versus no root; donor age; scalp origin; use of cosmetic hair treatments; and race of the donor. The results show that a positive correlation exists between amplification success and the presence of a telogen root. Combining the amplification success with either the original or optimized protocol, telogen hairs result in an overall success rate of 77.5% compared with 65% for hairs with no roots. Controlling for telogen hairs, the findings indicate that the overall success rate is independent of cosmetic hair treatments; medulla structure; shaft length, diameter, and volume; and scalp origin. Conversely, the age of the donor, the race of the donor, and hair pigmentation all contribute to a variation in amplification success rate.

A Taxonomy of Anger-Related Behaviors in Young Adults

In 2 studies, we investigated the occurrence of anger-related behaviors and their relationship to emotional, performance-related, and situational variables. In the first study, we constructed a comprehensive taxonomy of behaviors associated with anger, and we examined the occurrence of the resulting behavior categories as a function of several independent variables. A total of 8 distinct behavior categories were identified, 3 aggressive and 5 nonaggressive. Our results also demonstrated that fight (including both verbal and physical aggression) and flight behaviors occurred most frequently. Physical aggression, however, occurred most frequently in an inhibited form, in response to the emotion of anger (as compared to the emotion of irritation), and when the anger was intense. A second study was conducted to replicate and extend the findings of Study 1. The results suggest that the taxonomy, as derived in Study 1, is comprehensive and allows for a reliable categorization. Moreover, it appeared that fight and flight behaviors occurred most frequently if the target at whom one is angry was present.

Evaluation of measurement uncertainties of virtual instruments

This paper deals with measurement uncertainty of virtual instruments (VIs). First the main uncertainty sources of transducer, signal conditioning, A/D conversion and digital signal processing (DSP) are analyzed in detail. Two approaches to evaluate uncertainties of direct and indirect measurements are presented. The first approach deals with measuring an objective variable directly by application of a physical law. Its procedure includes: Step 1: the combined measurement uncertainties of transducer, signal conditioning, A/D conversion, and DSP are estimated respectively according to Type B evaluation of “guide to the expression of uncertainty in measurement (GUM)” based on Gram-Chariler series. Step 2: their corresponding relative measurement uncertainties are calculated, moreover the overall relative uncertainty of the direct measurement is evaluated in rms value. Step 3: the combined uncertainty of the direct measurement is estimated according to the measurement result and the value of overall relative uncertainty of the direct measurement. The second approach involves measurement of an objective variable that is a function of several independent variables; however these variables could be determined by direct respective measurements. The measurement uncertainty of the objective variable could be estimated by applying the “uncertainty propagation law” of GUM. Finally a case study is given to illustrate the application of these approaches.

ON SOBOLEV-VISIK-DUBINSKII TYPE INEQUALITIES


 
 
 In the present paper we establish some new integral inequalities of the Sobolev-Visik­ Dubinskii type involving functions of several independent variables and their first order partial derivatives. The analysis used in the proofs is elementary and the obtained results provide new estimates on these types of inequalities. 
 
 

Air Volume Migration from Negative Pressure Isolation Rooms during Entry/Exit

Abstract Negative-pressure isolation rooms (NPIRs) are used to isolate patients who have a suspected or known airborne infectious disease from the general hospital environment. When a person passes through an NPIR doorway, there exists an exchange of air between the isolation room and the area beyond its door. In a recent study, National Institute for Occupational Safety and Health researchers used sulfur hexafluoride tracer gas to examine the magnitude of air volume migration (AVM) as a function of several independent variables. A small cart carried a mannequin through a doorway separating a laboratory NPIR and a sulfur hexafluoride measurement chamber. The configuration provided simulated entry/exit of a healthcare worker through the doorway. Upon completion of experiments using a swinging door (including various cycle speeds for the door), a sliding door was installed and the experiments were repeated. In all cases examined, air flow rate differential between the air supplied to, and exhausted from, the NPIR was the only statistically significant factor in determining the level of AVM. Across the range of flow differentials examined (50 to 220 ft3/min), AVM ranged from 35 to 65 ft3. This range of AVM remained statistically unchanged regardless of door type, operating speed of the door, or entry to or exit from the NPIR. (Although entry/exit did significantly increase AVM, travel direction, whether entering or exiting the NPIR, did not.) By knowing the level of AVM during entry/exit through a doorway—a cause of airborne contaminant migration through a facility—a more complete assessment of the risk of transmission of an airborne infectious disease is made possible. This study shows that an anteroom or buffer zone outside the contaminated area's doorway will offer a degree of containment during entry/exit not otherwise obtainable. While this study concerned itself primarily with the engineering control of the transmission of airborne infectious diseases provided by ventilation systems, the results are applicable to any environment where a clean area is separated from a less clean area by a doorway. Hayden, II, C.S.; Johnston, O.E.; Hughes, R.T.; Jensen, P.A.: Air Volume Migration from Negative Pressure Isolation Rooms During Entry/Exit.

Computed Imaging-Assisted Stereotactic Brain Biopsy: A Risk Analysis of 225 Consecutive Cases

Background Treatment strategies for intracranial mass lesions are most effective when based upon histopathological diagnoses. Image-guided stereotaxy has provided the means to sample tissue from small or deeply seated intraparenchymal lesions with a relatively high degree of safety and accuracy. Although procedural complications are infrequent, devastating neurological sequelae may result from hemorrhage or direct trauma. This study was undertaken to identify factors that may confer an increased risk of morbidity from stereotactic brain biopsy. Methods Two hundred twenty-five consecutive computer-assisted stereotactic brain biopsy procedures were reviewed. Patient age averaged 47.4 years (range, 3–84 years); gender ratio was approximately 2:1 (male:female). Pre-existing medical conditions were identified in nearly half of the cohort. 61.3% of biopsied lesions were lobar; the remainder (38.7%) were “deep-seated” (thalamus, basal ganglia, pineal, hypothalamus, cerebellum, brainstem). Glial tumors accounted for the majority (44.4%) of biopsied lesions; metastases (12.9%) and lymphoma (11.6%) were also relatively common. Demographical, anatomical, surgical, and histological data were compiled and putative risk factors for morbidity identified. These variables were then subjected to univariate and logistic regression analyses to determine their significance as independent predictors of operative risk. Results Twelve patients suffered complications as a consequence of the biopsy procedure (eight from hemorrhage, four from direct trauma). Major morbidity (hemiparesis, aphasia, obtundation) occurred in eight patients (3.6%). Three patients (1.3%) suffered minor morbidity (transient, mild neurological deficits). One operative fatality occurred (0.4%). An increased risk of morbidity was associated with the preoperative use of antiplatelet agents, chronic corticosteroids, deep-seated lesions, malignant gliomas, and a greater number of biopsy attempts ( p < 0.05). Factors not conferring increased morbidity included gender, age, pre-existing illness, extracranial malignancy, cardiac disease, hypertension, diabetes, HIV status, and instrument used to procure the specimen. Conclusions Complications arising from stereotactic brain biopsy are infrequent but can be disastrous. Operative risk is a function of several independent variables, including lesion properties (location, histology), preoperative pharmacological therapy (corticosteroids, antiplatelet agents), and operative technique. This analysis suggests that the morbidity of stereotactic brain biopsy may be minimized by risk factor modification.

On a Nation of Resurgent Function of Several Variables

The Paper presents the definition of a resurgent a resurgent function of several independent variables. The main properties of the introduced notions are investigated.

Free Agency and the Allocation of Labor in Major League Baseball

AbstractIn this paper we examine the allocation of labor under free agency by developing and testing a model to predict the migration of free agents. Data for individual players are used in a logit model that estimates the probability that a free agent will change teams as a function of several independent variables. Along with other authors, we find that free agents tend to migrate to big cities. In addition, we find evidence that the allocation of labor may be different under free agency than under the reserve clause and suggest a reason why Coase's theorem may not be applicable to this labor market.

The lagrange multiplier rule for multi-dimensional problems of optimal control

In this paper a modified form of Pontryagin's maximum principle is developed, which also holds for problems of optimal control with respect to functions of several independent variables.

ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES

&#x0D; &#x0D; &#x0D; Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities. &#x0D; &#x0D; &#x0D;

ON MULTIDIMENSIONAL DISCRETE INEQUALITIES AND THEIR APPLICATIONS

&#x0D; &#x0D; &#x0D; The aim of the present paper is to establish some new multi-dimensional discrete inequalities which can be used as handy tools in the analysis of a new class of finite difference equations involving functions of several independent variables. &#x0D; &#x0D; &#x0D;

On Sobolev type integral inequalities

SynopsisThe aim of this paper is to establish some new integral inequalities of the Sobolev type involving functions of several independent variables. The analysis used in the proofs is elementary and the results established provide new estimates for this type of inequality.

Success in classical biological control

Classical biological control in the past has been characterized by numerous unsuccessful attempts and by relatively few outstanding successes. An analysis of the recent developments in the theoretical and applied aspects of classical biological control reveals, however, that introducing parasites (predators, pathogens, herbivores) against pest organisms apparently has a considerable potential of solving or lessening many important pest problems of the world. In this review, classical biological control was found to be applicable everywhere in the world regardless of temperature or moisture conditions, and native pests were found to be as susceptible to biological control as introduced pests. Biocontrol success was found to be a function of several independent variables (e.g., characteristics of the pest and control organism and the target ecosystem) and many dependent variables (e.g., the methods of selecting, propagating, and introducing the control organism). Knowledge about the interactions between these factors and other, external factors, will help to find probable ways of improving the success rate in introducing natural enemies. This has already been demonstrated by the steady increase in the efficiency of biocontrol work in the last 30 to 40 years.