Academic literature on the topic 'Continuous variation'

Functions of bounded variations form important transition between absolute continuous and singular functions. With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. However, the determination of existence of solutions is still problematic because the solutions of differential equations is usually at least absolute continuous which is disrupted by the solutions of bounded variations. As it is known, if f:[a,bλ]→Rn is of bounded variation then f is the sum of an absolute continuous function fa and a singular function fs where the total variation of fs generates a singular measure τ and fs is absolute continuous with respect to τ. In this paper we prove that a function of bounded variation f has two representations: one is f which was described with an absolute continuous part with respect to the Lebesgue measure λ, while in the other an integral with respect to τ forms the absolute continuous part and t(τ) defines the singular measure. Both representations are obtained as parameter transformation images of an absolute continuous function on total variation domain [a,bν].

ABSTRACTSociolinguists disagree on how to characterize diglossia with respect to the structural relatedness of the H(igh) and L(ow) varieties: Ferguson 1959, 1991 holds that H and L should be distinct but related varieties of language, while others maintain that a continuum model is more appropriate. Both discrete models (Gair 1968, 1992) and continuum models (De Silva 1974, 1979) have been proposed for Sinhala, as spoken in Sri Lanka. In this article, I employ a computer-generated multidimensional graph of relations between varieties of Sinhala to show that the distribution of H and L grammatical features in a sample of naturally occurring texts supports the discrete H and L model more than the continuum model. A rigorous characterization of diglossia as a distinct type of language situation is proposed, based on the notion “functional diasystem.” (Diglossia, Sinhala, Sri Lanka, diasystem, hybridization, continuum, South Asia, standardization)

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so that ignorance of their nature is profound.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management; and, Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1998.
Includes bibliographical references (p. 71).
by William C. Pack.
S.M.

Over the past 10 years, multiple executable modelling formalisms for molecular biology have been developed in order to address the growing need for a system-level understanding of complex biological phenomena. An important class of these formalisms are biology-inspired process algebras, which offer-among other desirable properties - an almost complete separation of model specification (syntax) from model dynamics (semantics). In this thesis, the similarity between this separation and the genotype-phenotype duality in evolutionary biology is exploited to develop a process-algebraic approach to the study of evolution of biochemical systems. The main technical contribution of this thesis is the continuous π-calculus (cπ), a novel process algebra based on the classical π-calculus of Milner et. al. Its two defining characteristics are: continuous, compositional, computationally inexpensive semantics, and a exible interaction structure of processes (molecules). Both these features are conductive to evolutionary analysis of biochemical systems by, respectively, enabling many variants of a given model to be evaluated, and facilitating in silico evolution of new functional connections. A further major contribution is a collection of variation operators, syntactic model transformation schemes corresponding to common evolutionary events. When applied to a cπ model of a biochemical system, variation operators produce its evolutionary neighbours, yielding insights into the local fitness landscape and neutral neighbourhood. Two well-known biochemical systems are modelled in this dissertation to validate the developed theory. One is the KaiABC circadian clock in the cyanobacterium S. elongatus, the other is a mitogen-activated protein kinase cascade. In each case we study the system itself as well as its predicted evolutionary variants. Simpler examples, particularly that of a generic enzymatic reaction, are used throughout the thesis to illustrate important concepts as they are introduced.

Continuous fermentations were performed in a novel external-recycle, biofilm reactor using D-glucose and CO2 as carbon substrates. Corn steep liquor (CSL) and yeast extract (YE) served as nitrogen sources. In anaerobic fermentations using medium containing CSL and YE, succinic acid (SA) yields were found to be an increasing function of glucose consumption. The ratio of SA to the major by-product, acetic acid (YAASA), increased from 2.4 g g-1 at a glucose consumption of 15 g L-1, to 5.7 g g-1 at a glucose consumption of 46 g L-1. For medium containing no CSL, YAASA remained near 1.97 g g-1, exceeding this for cases where biofilm grown on CSL-containing medium was present. The ratio of formic acid to acetic acid (YAAFA), for CSL-containing medium, decreased from an equimolar value (0.77 g g-1) at a glucose consumption of 10 g L-1 to zero at 46 g L-1 glucose consumed. In contrast, YAAFA for YE-only medium remained at 0.77 g g-1. Therefore, pyruvate was metabolised solely by pyruvate-formate lyase when no CSL was present. The highest SA yield obtained on glucose, SA titre and SA productivity were 0.91 g g-1, 48.5 g L-1 and 9.4 g L-1 h-1, respectively, all for medium containing CSL. Medium that included CSL significantly outperformed medium that excluded CSL, achieving 64%, 21% and 203% greater SA titres, yields on glucose and productivities respectively. Metabolic flux analyses based on the established C3 and C4 metabolic pathways of Actinobacillus succinogenes revealed that the increase in YAASA, for CSL-containing fermentations, could not be attributed to the decrease in formate and biomass formation, and that an additional source of reducing power was present. The fraction of reducing power (NADH) unaccounted for increased with glucose consumption, suggesting that the maintenance or non-growth metabolism encountered at higher SA titres differs from the growth metabolism. It is postulated that the additional reducing power originates from an active pentose phosphate pathway in non-growing cells or from an undetected component(s) in the fermentation medium. No major metabolic flux variations were found in fermentations that excluded CSL.
Dissertation (MEng)--University of Pretoria, 2013.
gm2014
Chemical Engineering
unrestricted

This paper presents an investigation on using the variation of ferrostatic pressure exerted by the molten steel in the strand to the support rolls during continuous casting to detect the location of the final solidification. The final solidification point is of high importance for applying soft reduction during continuous casting in order to ensure inner quality and achieve high productivity. The measurement was conducted at one of the casters at SSAB Oxelösund, of which all the support rolls are separately mounted. The project finds that this method shows promising results and can help to narrow down the range of the location due to certain interferences and noises. The ferrostatic pressure decrease during tail-out and the variation of whether a pressure drop exists is the dividing line of full and partial solidification. With the promising results achieved, more effort should be put to further improve the method.

In recent years, with the advance of computing equipment and image acquisition techniques, the sizes, dimensions and content of acquired images have increased considerably. Unfortunately as time passes there is a steadily increasing gap between the classical and parallel programming paradigms and their actual performance on modern computer hardware. In this thesis we consider in depth one particular algorithm, the continuous maximum flow computation. We review in detail why this algorithm is useful and interesting, and we propose efficient and portable implementations on various architectures. We also examine how it performs in the terms of segmentation quality on some recent problems of materials science and nano-scale biology

Thesis (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management; and, (S.M. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; in conjunction with the Leaders for Manufacturing Program at MIT, 2006.
Includes bibliographical references (leaf 58).
Intel's FAB 17 (F17), in an effort to remain competitive and reduce production cycle time, recently committed to adopt lean manufacturing as their approach to continuous improvement. To aid in this effort, the factory staff has dedicated a group people to develop tools based on lean manufacturing principles. Over the last 18 months, they have created three systematic approaches to address various forms of throughput variation, Autonomous Manufacturing (AM), Planned Maintenance (PM), and Waste Elimination (WE). Autonomous Manufacturing focuses on refurbishing manufacturing tools to new or better condition, up-skilling manufacturing technicians, and differentiating abnormal from normal operating conditions. It is meant to address throughput variation as a direct result of old, poorly maintained tools. Planned Maintenance focuses on keeping refurbished tools in new or better conditions, level loading maintenance activities, and minimizing manufacturing tool downtime due to scheduled maintenance activities. It is meant to address throughput variation as a direct result of tool availability variation. Finally, Waste Elimination focuses on optimizing the flow of information, people, and material.
(cont.) It is meant to address throughput variation as a direct result of inefficient flow through the manufacturing process. This thesis provides an overview of F17's lean journey. It shows that F17 has done an excellent job of developing an infrastructure to support their lean transformation. Going forward, their major challenge will be ingraining the new principles into the existing organizational structure. A variation analysis approach uses a simple model of daily production of an operation, several key metrics that relate work in progress (WIP) flow to tool performance, and a graphical display of WIP flow and tool performance. A case study conducted identifies the most probable source of throughput variation as arrivals at one operation, tool performance at another operation, and WIP management at a third operation.
by Sean Michael Holly.
S.M.in Ocean Engineering
M.B.A.

Investigations of detonative combustion of kerosene in air in flow-type combustors are of significant interest for science and applications. Detonative combustion of cold kerosene and diesel oil was earlier reached for the first time in a plane-radial combustor with a diameter dc1 = 204 mm. In annular cylindrical combustors, detonative combustion was obtained only if air was enriched with oxygen or if kerosene was enriched with hydrogen; another possible option was addition of isopropyl nitrate to kerosene.

In additive construction, ambitious goals to fabricate a concrete building in less than 24 hours are attempted. In the field, this goal relies on a metric of print time to make this conclusion, which excludes rest time and delays. The task to complete a building in 24 hours was put to the test with the first attempt at a fully continuous print of a structurally reinforced additively constructed concrete (ACC) building. A time series analysis was performed during the construction of a 512 ft2 (16’x32’x9.25’) building to explore the effect of delays on the completion time. This analysis included a study of the variation in comprehensive layer print times, expected trends and forecasting for what is expected in future prints of similar types. Furthermore, the study included a determination and comparison of print time, elapsed time, and construction time, as well as a look at the effect of environmental conditions on the delay events. Upon finishing, the analysis concluded that the 3D-printed building was completed in 14-hours of print time, 31.2- hours elapsed time, a total of 5 days of construction time. This emphasizes that reports on newly 3D-printed constructions need to provide a definition of time that includes all possible duration periods to communicate realistic capabilities of this new technology.

In this report the current air quality in Finland has been assessed with air quality measurement data and satellite observations. The assessment of ambient air concentrations included following air impurities: NO2, NOx, PM10, PM2,5, SO2, CO, O3, benzo(a)pyrene, benzene, Pb, As, Cd ja Ni. For these pollutants air quality assessment thresholds are given in air quality legislation (2008/50/EY, 2004/107/EY). Assessment has been performed for air quality zones. The main data set included air quality measurements performed in Finland during 2015–2019. Satellite observations were used as an objective assessment tool in analysis of the spatial variation of NO2 and CO concentrations. Air quality measurements show that air quality has improved in Finland in many respects. Especially the need to monitor NO2 and PM10 with continuous measurements has decreased. Growing understanding of national benzo(a)pyrene concentrations has increased the monitoring needs. Efforts to decrease ozone levels still requires international actions. SO2, CO, benzene and heavy metal concentrations are on a low level in Finland outside industrial areas and other assessment methods than continuous monitoring can be used, and the number of continuous monitoring sites has already decreased. Satellite-based concentrations of nitrogen dioxide and carbon monoxide as well as their spatial variation in Finland were analyzed using observations from the TROPOsperic Monitoring Instrument (TROPOMI). The analysis of CO over Finland was carried out for the first time in this project. Results show that overall annual CO concentrations over Finland are low and spatial variability is small. Also, NO2 concentrations over Finland are rather low, but spatial patterns are more clearly visible. The highest NO2 concentrations are observed over the largest cities. By establishing a relationship between ground-based and satellite total column concentrations, surface concentrations of NO2 and CO were estimated from the satellite data for the zones. The satellite-based estimate for annual NO2 surface concentration over Helsinki metropolitan area is 28 μg/m3, and for the rest of Finland mostly between 10–15 μg/m3. For CO the differences between monitoring areas are small, with estimates varying between 160–164 μg/m3 or in other words about 0,16 mg/m3.

This study examines the collaborative processes the Chicago Alliance for Equity in Computer Science (CAFÉCS) uses to conduct and use research. The CAFÉCS RPP is a partnership between Chicago Public Schools (CPS), Loyola University Chicago, The Learning Partnership, DePaul University, and University of Illinois at Chicago. Data used in this analysis comes from three years of evaluation data, and includes an analysis of team documents, meeting observations, and interviews with 25 members of the CAFÉCS RPP team. The analysis examines how three problems are being investigated by the partnership: 1) student failure rate in an introductory computer science course, 2) teachers’ limited use of discussion techniques in an introductory computer science class, and 3) computer science teacher retention. Results from the analysis indicate that the RPP engages in a formalized problem-solving cycle. The problem-solving cycle includes the following steps: First, the Office of Computer Science (OCS) identifies a problem. Next, the CAFÉCS team brainstorms and prioritizes hypotheses to test. Next, data analysis clarifies the problem and the research findings are shared and interpreted by the entire team. Finally, the findings are used to inform OCS improvement strategies and next steps for the CAFÉCS research agenda. There are slight variations in the problem-solving cycle, depending on the stage of understanding of the problem, which has implications for the mode of research (e.g hypothesis testing, research and design, continuous improvement, or evaluation).

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.

Meeting the increasingly stringent emission and fuel efficiency standards is the primary objective of the automotive research. Lean/diluted combustion is a promising avenue to realize high-efficiency combustion and reduce emissions in SI engines. Under the diluted conditions, the flame propagation speed is reduced because of the reduced charge reactivity. Enhancing the in-cylinder charge motion and turbulence, and thereby increasing the flame speed, is a possible way to harness the combustion process in SI engines. However, the charge motion can have a significant effect on the spark ignition process because of the reduced discharge duration and frequent restrikes. A longer discharge duration can aid in the formation of the self-sustained flame kernel and subsequent stable ignition. Therefore, an empirical study is undertaken to investigate the effect of the discharge duration and ignition timing on the ignition and early combustion in a port fueled SI engine, operated under lean conditions. The discharge duration is modulated from 1 ms to 8 ms through a continuous discharge strategy. The discharge current and voltage measurements are recorded during the engine operation to characterize the discharge process. The in-cylinder charge is diluted using fresh air to achieve lean combustion. The in-cylinder pressure measurement and heat release analysis are used to investigate the ignition and combustion characteristics of the engine. Preliminary results indicate that while the discharge duration has a marginal effect on the ignition delay, cyclic variations are notably impacted.