This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
This study aimed to examine the surface and content validity of the Mentoring Function Scale for Novice Nurses, used to assess the mentoring of entry-level nurses, and to refine the scale items. In Study 1, six nurse ...This study aimed to examine the surface and content validity of the Mentoring Function Scale for Novice Nurses, used to assess the mentoring of entry-level nurses, and to refine the scale items. In Study 1, six nurse education researchers, selected using convenience sampling, with five or more years of nursing experience and experience teaching novice nurses, were invited to an expert meeting in July 2015. A group interview was conducted that lasted approximately 120 minutes. Study 2 examined the content validity index. Between September and November 2015, we distributed a self-administered questionnaire survey to 11 participants selected by convenience sampling. The participants included five nurse education researchers with a minimum of five years of nursing experience and experience teaching novice nurses, as well as six clinical nurses with a master’s degree or higher. Finally, 81 questionnaire items were retained from the initial 125 items. The 81-item Mentoring Function Scale for Novice Nurses had higher content validity than the original scale. To further increase the scale’s applicability, future studies should assess its reliability, construct validity, and criterion-related validity.展开更多
Some studies have shown that left ventricular structure and function play an important role in the risk stratifi cation and prognosis of cardiovascular disease.The clinical application of left atrial function in cardi...Some studies have shown that left ventricular structure and function play an important role in the risk stratifi cation and prognosis of cardiovascular disease.The clinical application of left atrial function in cardiovascular disease has gradually attracted attention in the cardiovascular fi eld.There are many traditional methods to evaluate left atrial function.Left atrial function related indexes measured by echocardiography has been identifi ed as a powerful predictor of cardiovascular disease in recent years,but they have some limitations.The left atrial function index has been found to evaluate left atrial function more effectively than traditional parameters.Furthermore,it is a valuable predictor of the risk stratifi cation and prognosis in patients with clinical cardiovascular disease such as heart failure,atrial fi brillation,hypertension,and coronary heart disease.展开更多
Background: The aim of this study was to determine the relation of left atrial (LA) volume and LA volume index with left ventricular function and to determine the association of duration of symptoms and left atrial vo...Background: The aim of this study was to determine the relation of left atrial (LA) volume and LA volume index with left ventricular function and to determine the association of duration of symptoms and left atrial volume index in patients with dilated cardiomyopathy. Materials and Methods: This was an observational, single centre study conducted in India. A total of 50 patients who were admitted to department of cardiology from July, 2008 to February, 2009 with diagnosis of dilated cardiomyopathy and an ejection fraction of <40% were included. Results: Of the 50 patients, 34 (68%) were males. 27 (54%) patients were in NYHA class II and 23 (46%) patients were in NYHA class III. LA volume was found to be ≥40 ml in all patients. LV function and LA volume were found to be correlated (r = -0.789, p < 0.01). Similarly, there was a correlation between LV function and LA volume index (r = -0.826, p < 0.01). There was no correlation between LA volume index and duration of symptoms (r = 0.04). Conclusion: It can be concluded that there is a strong inverse correlation between LA volume and left ventricular function and also between LA volume index and left ventricular function. The patients with NYHA class III were having larger left atrial volume than those with NYHA class II. Moreover, the duration of symptoms has no correlation with left atrial volume index.展开更多
AIM: To evaluate the body mass index(BMI) change in arthroplasty patients and its impact on the patients' functional results. METHODS: Between October 2010 and May 2013, 606 patients who were operated due to gonar...AIM: To evaluate the body mass index(BMI) change in arthroplasty patients and its impact on the patients' functional results. METHODS: Between October 2010 and May 2013, 606 patients who were operated due to gonarthrosis, coxarthrosis, aseptic loosening of the total knee and hip prosthesis were evaluated prospectively. Patients were operated by three surgeons in three medical centers. Patients who were between 30-90 years of age and who were underwent total knee arthroplasty, total hip arthroplasty, revision knee arthroplasty, or revision hip arthroplasty were included in the study. We excluded the patients who cannot tolerate our standard postoperative rehabilitation program. Additionally, patients who had systemic inflammatory diseases, diabetes mellitus, or endochrinopathies were excluded from the study. The remaining 513 patients comprised our study group. Preoperative functional joint scores, height, weightand BMI of all patients were recorded. We used the Knee Society Score(KSS) for knee and Harris Hip Score(HHS) for hip patients. Postoperative functional scores were measured at 1^(st), 6^(th) and 12^(th) months and recorded separately at outpatient visits. RESULTS: The mean age of the patients was 64.7(range: 30-90) years(207 males/306 females) and the mean follow-up duration was 14.3(range: 12-26) mo. We found that arthroplasty patients had weight gain and had an increase in BMI at the postoperative 1^(st), 6^(th) and 12^(th) months. The mean BMI of the patients was 27.7 preoperatively, 27.8 at the postoperative 1^(st) month, 28.1 at the 6^(th) month and 28.6 at the 12^(th) month(P < 0.01). At the last visit, the mean postoperative HHS of the hip arthroplasty patients was 82.2 ± 7.12(preoperatively, 52.3; 1st month, 78.2; 6^(th) month, 81.1; 12^(th) month, 82.2), and the mean KSS of the knee arthroplasty patients was 79.3 ± 4.31(preoperatively, 35.8; 1^(st) month, 75.2; 6^(th) month, 79.1; 12^(th) month, 79.3). Worse functional results were noted in the patients who had a BMI increase, however, this correlation was statistically significant only at the postoperative 6^(th) month(P = 0.03). CONCLUSION: To prevent the negative functional effects of this weight gain during the postoperative period, arthroplasty patients should be advised for weight control and risky patients should consult with a dietician.展开更多
Background: To those patients with advanced lung cancer, the ultimate objective is to improve the quality of life, and lung function is an important factor affecting quality of life. We detect lung function of patient...Background: To those patients with advanced lung cancer, the ultimate objective is to improve the quality of life, and lung function is an important factor affecting quality of life. We detect lung function of patients with lung cancer and study the correlation between lung function and the patients’ survival time, to provide reference for evaluation of disease progression and prognosis. Methods: Lung function was detected on 59 cases of lung cancer and 63 normal controls. The relationship between lung function indexes and survival time was analyzed. Results: There was significant difference in ventilation function and diffusing capacity between lung cancer group and control group. Vital capacity (VC), Forced expiratory volume in one second (FEV1), Forced vital capacity (FVC), peak expiratory flow (PEF), peak expiratory flow% (PEF%), Maximal ventilatory volume (MVV) were positively correlated to survival time in patients with advanced lung cancer (r = 0.28522064, 0.28053851, 0.28289252, 0.26908133, 0.26335034, 0.28409036, P 0.05), residual volume/total lung capacity was negatively correlated to survival time (r = ?0.30760097, P 0.05). Conclusions: The lung function decrease in the patients with lung cancer. Vital capacity (VC), Forced expiratory volume in one second (FEV1), Forced vital capacity (FVC), peak expiratory flow (PEF), peak expiratory flow% (PEF%), Maximal ventilatory volume (MVV), and residual volume/total lung capacity are correlated to survival time in patients with advanced lung cancer. The lung function indexes are important marker of prognosis of patients with lung cancer.展开更多
AIM: To validate the culturally-adapted Persian Functional Rating Index(PFRI) for assessing neck pain(NP) in athletes. METHODS: In this cross-sectional study, 100 athletes with NP and 50 healthy athletes participated ...AIM: To validate the culturally-adapted Persian Functional Rating Index(PFRI) for assessing neck pain(NP) in athletes. METHODS: In this cross-sectional study, 100 athletes with NP and 50 healthy athletes participated and responded to the PFRI. Fifty athletes with NP completed the PFRI for at least 7 d later to establish test-retest reliability. RESULTS: The athletes with NP responded to all items, indicating excellent clinical utility. No floor and ceiling effects were found, indicating content validity and responsiveness. The PFRI revealed capability to discriminate between the athletes with NP and healthy athletes. The PFRI demonstrated strong correlation with the Numerical Rating Scale(Spearman's rho = 0.94), and the Persian Neck Disability Index(Pearson r = 0.995), supporting criterion and construct validity. Internal consistency reliability was high(Cronbach's α coefficient: 0.97). The test-retest reliability was excellent(ICCagreement = 0.96). The absolute reliability values of standard error of measurement and smallest detectable change were 3.2 and 8.84, respectively. An exploratory factor analysis yielded one factor explaining 78.03% of the total variance. CONCLUSION: The PFRI is a valid and reliable measure of functional status in athletes with NP.展开更多
Background: Reduced kidney function in blacks is associated with an increased frequency of left ventricular hypertrophy. Given the unavailability of echocardiography in most developing countries, the diagnostic perfor...Background: Reduced kidney function in blacks is associated with an increased frequency of left ventricular hypertrophy. Given the unavailability of echocardiography in most developing countries, the diagnostic performance of current ECG indexes needs to be evaluated. Objective: To compare the diagnostic performance of 3 commonly used ECG indexes (Sokolow-Lyon, Cornell voltage and Cornell product) in black hypertensive patients. Methods: Electrocardiography and echocardiography estimated left ventricular mass of 155 consecutive hypertensive patients who participated from January 2012 to January 2013 to an echocardiographic cross-sectional study of left ventricular structure was analyzed to compare Cornell voltage and Cornell product indexes with Sokolow-Lyon voltage index as a reference. Reduced kidney function was defined as eGFR 2. ROC curves in relation to LVH diagnosis were used to estimate the sensitivities and specificities of each index. P Results: The sensitivity and specificity were 43% and 85%, 23% and 77% and 26% and 77% for Sokolow-Lyon, Cornell voltage and Cornell product indexes, respectively. However, Sokolow-Lyon index (AUC;95% CI: 0.64;0.50 - 0.78) showed better performance than Cornell voltage (0.42;0.25 - 0.59) and Cornell product (0.43;0.28 - 0.59). Sokolow-Lyon index cut-point ≥ 37 mm corresponded to the highest Youden index (39.4% of sensitivity and 92.3% of specificity). Conclusion: Although the overall performance of the 3 ECG indexes versus echocardiography was low, Sokolow-Lyon index performed better than the two other indexes in diagnosing LVH.展开更多
In this paper we examine 5 indexes (the two Yule’s indexes, the chi square, the odds ratio and an elementary index) of a two-by-two table, which estimate the correlation coefficient ρ in a bivariate Bernoulli distri...In this paper we examine 5 indexes (the two Yule’s indexes, the chi square, the odds ratio and an elementary index) of a two-by-two table, which estimate the correlation coefficient ρ in a bivariate Bernoulli distribution. We will find the compact expression of the influence functions, which allow the quantification of the effect of an infinitesimal contamination of the probability of any pair of attributes of the bivariate random variable distributed according to the above-mentioned model. We prove that the only unbiased index is the chi square. In order to determine the indexes, which are less sensitive to contamination, we obtain the expressions of three synthetic measures of the influence function, which are the maximum contamination (gross sensitivity error), the mean square deviation and the variance. These results, even if don’t allow a definitive assessment of the overall optimum properties of the five indexes, as not all of them are unbiased, nevertheless they allow to appreciating the synthetic entity of the effect of the contaminations in the estimation of the parameter ρ of the bivariate Bernoulli distribution.展开更多
Objective: The objective of this study was to investigate the relationship between the triglyceride-glucose (TyG) index, triglyceride-glucose-BMI (TyG-BMI) index, laboratory indices, and disease severity in patients w...Objective: The objective of this study was to investigate the relationship between the triglyceride-glucose (TyG) index, triglyceride-glucose-BMI (TyG-BMI) index, laboratory indices, and disease severity in patients with COVID-19. Methods: A retrospective analysis of COVID-19 patients treated at a tertiary hospital in Mianyang City, Sichuan Province, China, from 1 May to 31 May 2023 was performed. The patients were divided into two groups: 66 cases in the moderate group and 61 cases in the severe group. Additionally, 69 uninfected individuals from the medical examination center during the same period were selected as the control group. Spearman rank correlation was used to determine the correlation between the indices and COVID-19 severity. Multiple logistic regression analysis was performed to identify the factors affecting COVID-19 severity. ROC curves were constructed to assess the predictive value of the TyG and TyG-BMI indices for severe COVID-19. Results: There were significant differences in smoking and diabetes between the three groups (P Conclusion: Smoking, AST, ALB, TyG index, and TyG-BMI index are valuable in assessing the severity of COVID-19, with the TyG-BMI index having a higher predictive value than the TyG index.展开更多
The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and...The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and the Vulnerability Index Indicator (VII) of a computer operating network. Both of these functions, VIF and VII are entities of the stochastic process that we have identified, which characterizes the probabilistic behavior of the number of vulnerabilities of a computer operating network. The VIF identifies the rate at which the number of vulnerabilities changes with respect to time. The VII is an important index indicator that conveys the following information about the number of vulnerabilities of Desktop Operating Systems: the numbers are increasing, decreasing, or remaining the same at a particular time of interest. This decision type of index indicator is crucial in every strategic planning and decision-making. The proposed VIF and VII illustrate their importance by using real data for Microsoft Windows Operating Systems 10, 8, 7, and Apple MacOS. The results of the actual data attest to the importance of VIF and VII in the cybersecurity problem we are currently facing.展开更多
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘This study aimed to examine the surface and content validity of the Mentoring Function Scale for Novice Nurses, used to assess the mentoring of entry-level nurses, and to refine the scale items. In Study 1, six nurse education researchers, selected using convenience sampling, with five or more years of nursing experience and experience teaching novice nurses, were invited to an expert meeting in July 2015. A group interview was conducted that lasted approximately 120 minutes. Study 2 examined the content validity index. Between September and November 2015, we distributed a self-administered questionnaire survey to 11 participants selected by convenience sampling. The participants included five nurse education researchers with a minimum of five years of nursing experience and experience teaching novice nurses, as well as six clinical nurses with a master’s degree or higher. Finally, 81 questionnaire items were retained from the initial 125 items. The 81-item Mentoring Function Scale for Novice Nurses had higher content validity than the original scale. To further increase the scale’s applicability, future studies should assess its reliability, construct validity, and criterion-related validity.
基金This work was supported by grants from the National Natural Science Foundation of China(81800056),the Science&Technology Development Fund of Tianjin Education Commission for Higher Education(2017KJ137),and the Key Research and Development Program of Hunan Province(2019SK2021).Scientifi c research project approved by Hunan Provincial Health Commission(202103012117).
文摘Some studies have shown that left ventricular structure and function play an important role in the risk stratifi cation and prognosis of cardiovascular disease.The clinical application of left atrial function in cardiovascular disease has gradually attracted attention in the cardiovascular fi eld.There are many traditional methods to evaluate left atrial function.Left atrial function related indexes measured by echocardiography has been identifi ed as a powerful predictor of cardiovascular disease in recent years,but they have some limitations.The left atrial function index has been found to evaluate left atrial function more effectively than traditional parameters.Furthermore,it is a valuable predictor of the risk stratifi cation and prognosis in patients with clinical cardiovascular disease such as heart failure,atrial fi brillation,hypertension,and coronary heart disease.
文摘Background: The aim of this study was to determine the relation of left atrial (LA) volume and LA volume index with left ventricular function and to determine the association of duration of symptoms and left atrial volume index in patients with dilated cardiomyopathy. Materials and Methods: This was an observational, single centre study conducted in India. A total of 50 patients who were admitted to department of cardiology from July, 2008 to February, 2009 with diagnosis of dilated cardiomyopathy and an ejection fraction of <40% were included. Results: Of the 50 patients, 34 (68%) were males. 27 (54%) patients were in NYHA class II and 23 (46%) patients were in NYHA class III. LA volume was found to be ≥40 ml in all patients. LV function and LA volume were found to be correlated (r = -0.789, p < 0.01). Similarly, there was a correlation between LV function and LA volume index (r = -0.826, p < 0.01). There was no correlation between LA volume index and duration of symptoms (r = 0.04). Conclusion: It can be concluded that there is a strong inverse correlation between LA volume and left ventricular function and also between LA volume index and left ventricular function. The patients with NYHA class III were having larger left atrial volume than those with NYHA class II. Moreover, the duration of symptoms has no correlation with left atrial volume index.
文摘AIM: To evaluate the body mass index(BMI) change in arthroplasty patients and its impact on the patients' functional results. METHODS: Between October 2010 and May 2013, 606 patients who were operated due to gonarthrosis, coxarthrosis, aseptic loosening of the total knee and hip prosthesis were evaluated prospectively. Patients were operated by three surgeons in three medical centers. Patients who were between 30-90 years of age and who were underwent total knee arthroplasty, total hip arthroplasty, revision knee arthroplasty, or revision hip arthroplasty were included in the study. We excluded the patients who cannot tolerate our standard postoperative rehabilitation program. Additionally, patients who had systemic inflammatory diseases, diabetes mellitus, or endochrinopathies were excluded from the study. The remaining 513 patients comprised our study group. Preoperative functional joint scores, height, weightand BMI of all patients were recorded. We used the Knee Society Score(KSS) for knee and Harris Hip Score(HHS) for hip patients. Postoperative functional scores were measured at 1^(st), 6^(th) and 12^(th) months and recorded separately at outpatient visits. RESULTS: The mean age of the patients was 64.7(range: 30-90) years(207 males/306 females) and the mean follow-up duration was 14.3(range: 12-26) mo. We found that arthroplasty patients had weight gain and had an increase in BMI at the postoperative 1^(st), 6^(th) and 12^(th) months. The mean BMI of the patients was 27.7 preoperatively, 27.8 at the postoperative 1^(st) month, 28.1 at the 6^(th) month and 28.6 at the 12^(th) month(P < 0.01). At the last visit, the mean postoperative HHS of the hip arthroplasty patients was 82.2 ± 7.12(preoperatively, 52.3; 1st month, 78.2; 6^(th) month, 81.1; 12^(th) month, 82.2), and the mean KSS of the knee arthroplasty patients was 79.3 ± 4.31(preoperatively, 35.8; 1^(st) month, 75.2; 6^(th) month, 79.1; 12^(th) month, 79.3). Worse functional results were noted in the patients who had a BMI increase, however, this correlation was statistically significant only at the postoperative 6^(th) month(P = 0.03). CONCLUSION: To prevent the negative functional effects of this weight gain during the postoperative period, arthroplasty patients should be advised for weight control and risky patients should consult with a dietician.
文摘Background: To those patients with advanced lung cancer, the ultimate objective is to improve the quality of life, and lung function is an important factor affecting quality of life. We detect lung function of patients with lung cancer and study the correlation between lung function and the patients’ survival time, to provide reference for evaluation of disease progression and prognosis. Methods: Lung function was detected on 59 cases of lung cancer and 63 normal controls. The relationship between lung function indexes and survival time was analyzed. Results: There was significant difference in ventilation function and diffusing capacity between lung cancer group and control group. Vital capacity (VC), Forced expiratory volume in one second (FEV1), Forced vital capacity (FVC), peak expiratory flow (PEF), peak expiratory flow% (PEF%), Maximal ventilatory volume (MVV) were positively correlated to survival time in patients with advanced lung cancer (r = 0.28522064, 0.28053851, 0.28289252, 0.26908133, 0.26335034, 0.28409036, P 0.05), residual volume/total lung capacity was negatively correlated to survival time (r = ?0.30760097, P 0.05). Conclusions: The lung function decrease in the patients with lung cancer. Vital capacity (VC), Forced expiratory volume in one second (FEV1), Forced vital capacity (FVC), peak expiratory flow (PEF), peak expiratory flow% (PEF%), Maximal ventilatory volume (MVV), and residual volume/total lung capacity are correlated to survival time in patients with advanced lung cancer. The lung function indexes are important marker of prognosis of patients with lung cancer.
文摘AIM: To validate the culturally-adapted Persian Functional Rating Index(PFRI) for assessing neck pain(NP) in athletes. METHODS: In this cross-sectional study, 100 athletes with NP and 50 healthy athletes participated and responded to the PFRI. Fifty athletes with NP completed the PFRI for at least 7 d later to establish test-retest reliability. RESULTS: The athletes with NP responded to all items, indicating excellent clinical utility. No floor and ceiling effects were found, indicating content validity and responsiveness. The PFRI revealed capability to discriminate between the athletes with NP and healthy athletes. The PFRI demonstrated strong correlation with the Numerical Rating Scale(Spearman's rho = 0.94), and the Persian Neck Disability Index(Pearson r = 0.995), supporting criterion and construct validity. Internal consistency reliability was high(Cronbach's α coefficient: 0.97). The test-retest reliability was excellent(ICCagreement = 0.96). The absolute reliability values of standard error of measurement and smallest detectable change were 3.2 and 8.84, respectively. An exploratory factor analysis yielded one factor explaining 78.03% of the total variance. CONCLUSION: The PFRI is a valid and reliable measure of functional status in athletes with NP.
文摘Background: Reduced kidney function in blacks is associated with an increased frequency of left ventricular hypertrophy. Given the unavailability of echocardiography in most developing countries, the diagnostic performance of current ECG indexes needs to be evaluated. Objective: To compare the diagnostic performance of 3 commonly used ECG indexes (Sokolow-Lyon, Cornell voltage and Cornell product) in black hypertensive patients. Methods: Electrocardiography and echocardiography estimated left ventricular mass of 155 consecutive hypertensive patients who participated from January 2012 to January 2013 to an echocardiographic cross-sectional study of left ventricular structure was analyzed to compare Cornell voltage and Cornell product indexes with Sokolow-Lyon voltage index as a reference. Reduced kidney function was defined as eGFR 2. ROC curves in relation to LVH diagnosis were used to estimate the sensitivities and specificities of each index. P Results: The sensitivity and specificity were 43% and 85%, 23% and 77% and 26% and 77% for Sokolow-Lyon, Cornell voltage and Cornell product indexes, respectively. However, Sokolow-Lyon index (AUC;95% CI: 0.64;0.50 - 0.78) showed better performance than Cornell voltage (0.42;0.25 - 0.59) and Cornell product (0.43;0.28 - 0.59). Sokolow-Lyon index cut-point ≥ 37 mm corresponded to the highest Youden index (39.4% of sensitivity and 92.3% of specificity). Conclusion: Although the overall performance of the 3 ECG indexes versus echocardiography was low, Sokolow-Lyon index performed better than the two other indexes in diagnosing LVH.
文摘In this paper we examine 5 indexes (the two Yule’s indexes, the chi square, the odds ratio and an elementary index) of a two-by-two table, which estimate the correlation coefficient ρ in a bivariate Bernoulli distribution. We will find the compact expression of the influence functions, which allow the quantification of the effect of an infinitesimal contamination of the probability of any pair of attributes of the bivariate random variable distributed according to the above-mentioned model. We prove that the only unbiased index is the chi square. In order to determine the indexes, which are less sensitive to contamination, we obtain the expressions of three synthetic measures of the influence function, which are the maximum contamination (gross sensitivity error), the mean square deviation and the variance. These results, even if don’t allow a definitive assessment of the overall optimum properties of the five indexes, as not all of them are unbiased, nevertheless they allow to appreciating the synthetic entity of the effect of the contaminations in the estimation of the parameter ρ of the bivariate Bernoulli distribution.
文摘Objective: The objective of this study was to investigate the relationship between the triglyceride-glucose (TyG) index, triglyceride-glucose-BMI (TyG-BMI) index, laboratory indices, and disease severity in patients with COVID-19. Methods: A retrospective analysis of COVID-19 patients treated at a tertiary hospital in Mianyang City, Sichuan Province, China, from 1 May to 31 May 2023 was performed. The patients were divided into two groups: 66 cases in the moderate group and 61 cases in the severe group. Additionally, 69 uninfected individuals from the medical examination center during the same period were selected as the control group. Spearman rank correlation was used to determine the correlation between the indices and COVID-19 severity. Multiple logistic regression analysis was performed to identify the factors affecting COVID-19 severity. ROC curves were constructed to assess the predictive value of the TyG and TyG-BMI indices for severe COVID-19. Results: There were significant differences in smoking and diabetes between the three groups (P Conclusion: Smoking, AST, ALB, TyG index, and TyG-BMI index are valuable in assessing the severity of COVID-19, with the TyG-BMI index having a higher predictive value than the TyG index.
文摘The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and the Vulnerability Index Indicator (VII) of a computer operating network. Both of these functions, VIF and VII are entities of the stochastic process that we have identified, which characterizes the probabilistic behavior of the number of vulnerabilities of a computer operating network. The VIF identifies the rate at which the number of vulnerabilities changes with respect to time. The VII is an important index indicator that conveys the following information about the number of vulnerabilities of Desktop Operating Systems: the numbers are increasing, decreasing, or remaining the same at a particular time of interest. This decision type of index indicator is crucial in every strategic planning and decision-making. The proposed VIF and VII illustrate their importance by using real data for Microsoft Windows Operating Systems 10, 8, 7, and Apple MacOS. The results of the actual data attest to the importance of VIF and VII in the cybersecurity problem we are currently facing.