ap.analysis of pdes – Difference between two Fractional Schrödinger equation

Let us consider the fractional Schrödinger equation with periodic boundary conditions
iu_tmathbf{+}(-Delta)^{alpha}u= pm |u|^2u,; x in mathbb{T}, t in mathbb{R}_+\
u(x,0)=u_0(x), ; x in mathbb{T} tag{1}

where $mathbb{T} subset mathbb{R}$ is a torus, $u_0 in H^s(mathbb{T})$, $alpha in (1/2,1)$ and $s>0$. Also, in the same way, consider
iu_tmathbf{-}(-Delta)^{alpha}u= pm |u|^2u,; x in mathbb{T}, t in mathbb{R}_+\
u(x,0)=u_0(x), ; x in mathbb{T}. tag{2}

Question. What is difference between the equation $(1)$ and $(2)$? My question is the following sense: in $(1)$ the authors showed (see Theorem $2$) that the $(1)$ is globally well-posed in $H^s(mathbb{T})$ provided that $s> tfrac{10 alpha+1}{12}.$
In this way, is true the same result for the equation $(2)$? If no, why? It’s not clear to me what kind of properties the equation loses (or gains) by changing the sign. Note that, we are in a periodic context.
References are welcome.

$(1)$ S. Demirbas, M. B. Erdogan, and N. Tzirakis. Existence and uniqueness theory for the fractional Schrödinger equation on the torus. In Some topics in harmonic analysis and applications, volume $34$ of Adv. Lect. Math.(ALM), pages $145$$162$. Int. Press, Somerville, MA, $2016$.

20.04 – What is the difference between && and ; in multiple commands

Hello i am trying to run multiple commands at once in a single line of peace in ubuntu terminal

My first approach was command1 && command2 && command3 e.g. ls && whoami
My second approach was command1 ; command2 ; command3 e.g. ls;whoami

Although they did not put any major change at least not in my knowledge using both of above but i noticed it has some thing to do with commands execution flow! commands whose output is very large I noticed none of them works or execute next command the problem is a bit hard to reproduce the actual commands that are causing trouble are following

dotnet sonarscanner begin /k:"myKey" /d:sonar.scm.disabled=true /d:sonar.host.url="http://localhost:9000" && dotnet build myProject.sln && dotnet sonarscanner end

in above commands some time all commands execute sometime there is not any error firs two commands are executed not third one mostly when project has lot of output e.g. warnings or verbose output.

algebraic topology – Difference between bottleneck and matching distances

Can anyone explain me what’s the difference between matching and bottleneck distances?
I found a definition here where one is used for diagrams and one for the betti number function induced by the filtering function, and one here where they say that the two distances are the same thing.
I know this is a trivial question, but I’m honestly clueless and I don’t want to make mistakes for a wrong definition.

sharepoint rest api – What’s the difference between the fields “owshiddenversion” and “OData__UIVersion”?

Query is something like .../_api/web/Lists/GetByTitle('Documents')/items?$select=File,File/ServerRelativeUrl,OData__UIVersion,owshiddenversion,FileRef

This worked in a SP Root site: OData__UIVersion was the exact number of versions.

But in a subsite (the same SP), for a file with just one version, OData__UIVersion is 512

Next, I discovered the other field: owshiddenversion; This one seems to really return the correct value: the number of versions of a file.

Does anybody know what’s the official definition of these 2 fields ?
Is it safe to rely on owshiddenversion to determine how many versions a file has ?

Thank you.

seo – LocalBusiness Schema – difference between @id and @url

We include the localBusiness data across all pages on our ecommerce site.

What values should be set for id and url on different pages e.g.

  1. example.com/about-us
  2. example.com/shop
      "@context": "https://schema.org",
      "@type": "localBusiness",
      "@id": "http://example.com/current-page",
      "name": "Ecommerce Shop",
      "url": "http://www.example.com/"

Should id be based on the current url or should it be id?

magento2 – Difference between various default.xml

magento2 – Difference between various default.xml – Magento Stack Exchange

java – Difference between Efferent Coupling and Dependency Injection

I am working on research that analyzes dependency injection (DI) in Java projects. The more I read, the more I get confused by DI in relation to other frameworks and even software quality metrics.

I have been recently reading about afferent couplings (Ca), efferent couplings (Ce), and instability (I) with the formula below proposed by Martin Fowler:

I = (Ce/(Ce + Ca))

I noticed that the definition of efferent couplings is that it counts the number of classes the current class depends on. Is that essentially the same as dependency injection definition-wise, or are there more nuances to what is considered a dependency that has the DI framework as opposed to simply a class that the current class depends on?

visas – Difference between residence permit and common format residence permit

I am an Indian and have Netherlands residence Permit Type 1.
I am travelling from Amsterdam and will be transiting in LHR towards New delhi do I need transit visa?

In the exemptions it says if you have a common format residence permit issued by an European Economic Area then you do not need a transit visa.

Can I consider my Netherlands residence permit as common format residence permit or there is difference between the two?

Below are the flight details:
Flight details
BA431 Amsterdam –> London
BA257 London –> New Delhi


Marketing vs. Advertising: What’s the difference?

It may seem like advertising and marketing are two concepts that share exactly the same objective. In fact, they do have the same objective: alerting consumers to products and services being sold. Marketing and advertising have many things in common, but there are some differences. Comprehension of these differences and similarities will help any business or organization with their strategy for customer and audience acquisition.
Marketing is a process that involves design, creation, research and data mining about how to best align the idea of a product or service with the target audience. Marketing helps to define the product even more than the actual product does.
Marketing involves research and analysis. This involves studying audience response and creating language and design that will best influence that audience. Certain groups of consumers respond better to images and words than others. Slogans and mission statements that best communicate the “message” of the product are essential to marketing. Marketing strategy can be broken down into the 4 P’s: product, place, price and promotion.

The message of a marketing campaign transmits what kind of people can use the product, what kind of environment best suits the product and other related information. The message is communicated through marketing materials, which create tone and personality of the product as well. Another aspect of market research is pricing and ways to distribute the product.



difference equations – RecurrenceTable for computing Required Minimum Distributions from an IRA

Here is a list of required minimum distributions from an IRA based on IRS published life expectancy tables for a particular age

    rmd={5.12821, .34759, .58659, .84795, .13497, .45161, .75676, .09220, .46269}

One must withdraw the particular portion shown for subsequent years. The rate is applied to the value of the fund at prior year end (beginning with a starting balance). Assume the fund grows monotonically at 3% per year. Each distribution is the prior year end balance times 1.03 less the current year distribution (calculated on the prior year) times the particular rmd for that year. One would think a RecurrenceTable would be just the ticket but it does not like Part in the arguments to single out the particular rmd rate for a certain year. The answer in Excel is straightforward assuming no value change in the first year

Thanks for your help

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