Skip to main content

Cloud computing in engineering workflows

Cloud Computing in Engineering Workflows:   Transforming Design, Collaboration, and Innovation In today’s fast-paced engineering landscape, the need for speed, scalability, and seamless collaboration is greater than ever. Traditional engineering workflows often relied on on-premises servers, powerful local machines, and fragmented communication tools. But as projects grow in complexity and teams become more global, these systems can no longer keep up. This is where cloud computing steps in—reshaping how engineers design, simulate, collaborate, and deliver results. What is Cloud Computing in Engineering? Cloud computing refers to the use of remote servers hosted on the internet to store, process, and analyze data. Instead of being limited by the hardware capacity of a single computer or office server, engineers can leverage vast, scalable computing resources from cloud providers. This shift enables engineers to run simulations, share designs, and manage data more efficiently. Key Be...

Omega, Theta notation

OMEGA NOTATION (Ω)
The Omega notation provides a tight lower bound for f(n). This means that the function can never do better than the specified value but it may do worse. 
Ω notation is simply written as, f(n) ∈ Ω(g(n)), where n is the problem size and 
Ω(g(n)) = {h(n): ∃ positive constants c > 0, n0  such that 0 ≤ cg(n) ≤ h(n), ∀ n ≥ n0}.
Hence, we can say that Ω(g(n)) comprises a set of all the functions h(n) that are greater than or equal to cg(n) for all values of n ≥ n0.
If cg(n) ≤ f(n), c > O, ∀ n ≥ nO, then f(n) ∈ Ω(g(n)) and g(n) is an asymptotically tight 
lower bound for f(n).
Examples of functions in Ω(n2) include: n2, n2.9, n3+ n2, n3
Examples of functions not in Ω(n3) include: n, n2.9, n2
To summarize, 
• Best case Ω describes a lower bound for all combinations of input. This implies that the function can never get any better than the specified value. For example, when sorting an array the best case is when the array is already correctly sorted.
• Worst case Ω describes a lower bound for worst case input combinations. It is possibly greater than best case. For example, when sorting an array the worst case is when the array is sorted 
in reverse order.
• If we simply write Ω, it means same as best case Ω.

THETA NOTATION (Θ)
Theta notation provides an asymptotically tight bound for f(n). Θ notation is simply written as, 
f(n) ∈ Θ(g(n)), where n is the problem size and Θ(g(n)) = {h(n): ∃ positive constants c1, c2, and n0
 such that 0 ≤ c1g(n) ≤ h(n) ≤ c2
g(n), ∀ n ≥ n0}. 
Hence, we can say that Θ(g(n)) comprises a set of all the functions h(n) that are between c1g(n)and c2g(n) for all values of n ≥ n0.
If f(n) is between c1g(n) and c2g(n), ∀ n ≥ n0,then f(n) ∈ Θ(g(n)) and g(n) is an asymptotically tight bound for f(n) and f(n) is amongst h(n) in the set.
To summarize, 
• The best case in Θ notation is not used.
• Worst case Θ describes asymptotic bounds for worst case combination of input values. 
• If we simply write Θ, it means same as worst case Θ.

OTHER USEFUL NOTATIONS
There are other notations like little o notation and little ω notation which have been discussed below.
Little o Notation
This notation provides a non asymptotically tight upper bound for f(n). To express a function using this notation, we write 
f(n) ∈ o(g(n)) where
o(g(n)) = {h(n) : ∃ positive constants c, n0
 such that for any c > 0, n0 > 0, and 0 ≤ h(n) ≤ cg(n), ∀ n ≥ n0}.
This is unlike the Big O notation where we say for some c > 0 (not any). For example, 5n3 = O(n3) is asymptotically tight upper bound but 5n2 = o(n3) is non-asymptotically tight bound for f(n).
Examples of functions in o(n3) include: n2.9, n3 / log n, 2n2
Examples of functions not in o(n3) include: 3n3, n3, n3 / 1000

Little Omega Notation (w)
This notation provides a non-asymptotically tight lower bound for f(n). It can be simply written as,f(n) ∈ ω(g(n)), whereω(g(n)) = {h(n) : ∃ positive constants c, n0 such that for any c > 0, n0 > 0, and 0 ≤ cg(n) < h(n),∀ n ≥ n0}.
This is unlike the Ω notation where we say for some c > 0 (not any). For example, 5n3 = Ω(n3) is asymptotically tight upper bound but 5n2 = ω(n3) is non-asymptotically tight bound for f(n).
Example of functions in ω(g(n)) include: n3 = ω(n2), n3.001 = ω(n3), n2
logn = ω(n2)
Example of a function not in ω(g(n)) is 5n2 ≠ ω(n2) (just as 5≠5)
An imprecise analogy between the asymptotic comparison of functions f(n) and g(n) and the relation between their values can be given as:
f(n) = Ω(g(n)) ≈ f(n) ≥ g(n) f(n) = ω(g(n)) ≈ f(n) > g(n)

Popular posts from this blog

Abbreviations

No :1 Q. ECOSOC (UN) Ans. Economic and Social Commission No: 2 Q. ECM Ans. European Comman Market No : 3 Q. ECLA (UN) Ans. Economic Commission for Latin America No: 4 Q. ECE (UN) Ans. Economic Commission of Europe No: 5 Q. ECAFE (UN)  Ans. Economic Commission for Asia and the Far East No: 6 Q. CITU Ans. Centre of Indian Trade Union No: 7 Q. CIA Ans. Central Intelligence Agency No: 8 Q. CENTO Ans. Central Treaty Organization No: 9 Q. CBI Ans. Central Bureau of Investigation No: 10 Q. ASEAN Ans. Association of South - East Asian Nations No: 11 Q. AITUC Ans. All India Trade Union Congress No: 12 Q. AICC Ans. All India Congress Committee No: 13 Q. ADB Ans. Asian Development Bank No: 14 Q. EDC Ans. European Defence Community No: 15 Q. EEC Ans. European Economic Community No: 16 Q. FAO Ans. Food and Agriculture Organization No: 17 Q. FBI Ans. Federal Bureau of Investigation No: 18 Q. GATT Ans. General Agreement on Tariff and Trade No: 19 Q. GNLF Ans. Gorkha National Liberation Front No: ...

Operations on data structures

OPERATIONS ON DATA STRUCTURES This section discusses the different operations that can be execute on the different data structures before mentioned. Traversing It means to process each data item exactly once so that it can be processed. For example, to print the names of all the employees in a office. Searching It is used to detect the location of one or more data items that satisfy the given constraint. Such a data item may or may not be present in the given group of data items. For example, to find the names of all the students who secured 100 marks in mathematics. Inserting It is used to add new data items to the given list of data items. For example, to add the details of a new student who has lately joined the course. Deleting It means to delete a particular data item from the given collection of data items. For example, to delete the name of a employee who has left the office. Sorting Data items can be ordered in some order like ascending order or descending order depending ...

The Rise of Solar and Wind Energy: A Glimpse into a Sustainable Future

In the quest for a sustainable future, solar and wind energy systems have emerged as two of the most promising sources of renewable energy. As concerns about climate change and the depletion of fossil fuels grow, these technologies offer a pathway to a cleaner, more resilient energy grid. This blog post delves into the significance of solar and wind energy, their benefits, challenges, and the role they play in shaping a sustainable future. The Basics of Solar and Wind Energy Solar Energy Systems harness the power of the sun to generate electricity. The most common technology used is photovoltaic (PV) panels, which convert sunlight directly into electricity. Solar thermal systems, another approach, use mirrors or lenses to concentrate sunlight, generating heat that can be used to produce electricity. Solar energy is abundant, renewable, and available almost everywhere on Earth. Wind Energy Systems utilize wind turbines to convert the kinetic energy of wind into electrical energy. Thes...